In the Sanctification stage (Reformed perspective) are believers truly becoming more like Christ ("infusion" not imputed)?

I will be using Dr. William Downing's A Baptist Catechism as my source. He is a Reformed Baptist, though his position here is similar to most Reformed Presbyterians I have read on the matter.

I will begin by answering the question: No, there is no proper infusion of Christ's righteousness associated with the progressive nature of Sanctification.

First, I would not that there is a substantial distinction between the righteousness of God (which Christ possesses) and the righteousness that may be had by man, even in his complete sanctification. Downing, in his commentary on Q. 28 of the catechism describes God as "absolutely righteous". While Downing does not address Divine Simplicity in this catechism, it is ubiquitously affirmed throughout the Reformed divines of history. Thus, by divine simplicity, that is, God IS righteousness, there is no meaningful way in which a man may also possess or be infused with that righteousness, imputation remains as the only meaningful possibility.

But what of the progressive nature of this sanctification?

Q. 96: What are the two aspects of progressive or practical sanctification?

Ans: The two aspects of progressive or practical sanctification are the positive, or vivification, and the negative, or mortification of sin.

In his commentary on this question Downing answers many of the questions you offered in the OP. I'll leave the relevant sanction for you here:

Vivification. There are five elements which must be seriously considered in such sanctification or vivification: first, sin has been dethroned in every individual who has been effectually called, regenerated and converted, and thus, in everyone without exception who has been and is being sanctified. Believers are no longer under the dominating power of sin, but do commit acts of sin which must be dealt with (Rom. 6:11–14; 1 Jn. 2:1; 3:9). See Questions 114–115. The realities of union with Christ, effectual calling, regeneration and definitive sanctification must find appropriate expression in practical or progressive sanctification (Rom. 6:14; 2 Cor. 5:14–17; 1 Jn. 3:9; 1 Jn. 5:4, 18).

Second, professing believers are either subjects of the redemptive, transforming grace of God or they are graceless. There is no middle ground or place for a true Christian to continue to live in sin (Matt. 7:21–23; Acts 8:18– 24; 2 Cor. 13:5; 2 Tim. 4:10; Heb. 3:12–13; 12:7–8, 14–15).

Third, the agent or operating power in such sanctification is the Holy Spirit. Believers do not sanctify themselves in their own strength, although they are necessarily exhorted to godly living (2 Cor. 7:1; 1 Thess. 4:7; 1 Pet. 2:9). There is a gracious, operative dynamic which works to conform believers to the image of God’s Son in principle in the context of the eternal redemptive purpose (Rom. 6:14; 2 Cor. 3:17–18; Phil. 2:12–13).

Fourth, the goal of progressive sanctification is conformity to the moral character of God; specifically, conformity to the image of God’s Son (Rom. 8:29; 2 Cor. 3:17–18; 1 Pet. 1:15–16; 1 Jn. 3:1–4).

Fifth, there is an undeniable principle of progression in practical sanctification which the Scriptures clearly reveal. This progressive nature is due to the effectual work of the Holy Spirit. Thus, practical sanctification is most thoroughly described as progressive sanctification (Matt. 5:48; Rom. 12:2; 2 Cor. 7:1; Eph. 1:17–20; 3:14–19; 4:12–16; Phil. 1:9–11; 2:12–13; Col. 1:9–12; 2:6–7; 1 Pet. 1:15–16; 2:2; 2 Pet. 3:18; 1 Jn. 3:3).

Vivification may at times be feeble, static, and at times seem to even be in reverse, yet in the state of grace, such is an on–going reality. Sanctification can be illustrated by the southward flow of the Mississippi River. This river at times flows west, east and even north as it winds its way, but its tendency is south, and it ultimately flows south into the Gulf of Mexico. Divine correction is present in the form of conviction of sin and Divine chastis*m*nt (Heb. 12:4–13).

So in our sanctification, it is not an infusion of the righteousness of Christ, but rather a conformity to the image of that righteousness. The image of that righteousness that we have is the life of Christ in the Incarnation.

As for your concern about some sort of reliable measuring stick, we may find it in the churches exercise of Church Discipline.

From Downings commentary on Q. 163:

The word “discipline” is derived from the Latin, disco, “I learn”—hence the terms “disciple” or “learner,” and “discipline” or “teaching, training, submission.” The New Testament views the church as a disciplined body. The various members are to grow toward spiritual maturity individually and collectively. There is to be an increasing principle of unity pervading the congregation that is the result of such formative discipline. (1 Cor. 12:1–28; Eph. 2:21–22; 4:1–3, 11–16; 5:1–2, 21; 6:10–18; Phil. 1:9–11, 27; 2:1–5, 12– 16; 4:1–9; Col. 1:28–29; 2:6–7; 3:1–8; 2 Pet. 1:4–8; 3:18). This formative element is to manifest itself in what might be termed the “Christian Ethic” or “corporate sanctification” governing the relationship of believers to each other and to all within the assembly. (See Eph. 5:1–17; 6:5–9; Col. 3:22–25; Rom. 12, 17–21). See Question 94. Such formative discipline presupposes a church in which the Holy Spirit is actively at work in and through the proper ministry of the Word, and a church in which there is likewise the practice of corrective discipline.

We see similar language used in talking about church discipline as we do in talking about sanctification. Church discipline is one of the primary means for the mortification of sin.

If you have comments and questions, leave them and I will seek to continue improving my answer.

Edit: Responding to OP's question from Comments.

@GratefulDisciple writes:

1) clarification on righteousness vs. holiness in the sanctification stage: it seems righteousness is only imputed, which is clear for the justification stage, but in the Holy Spirit work of conforming us to Christ image, isn't believer being transformed in holiness, so the question is whether this holiness if infused/imputed?

When we speak of Sanctification in progressive terms, we must make an identification between righteousness and holiness. Properly, "Holiness" is only a declaration that something has been "set apart". So when we talk about progressive holiness, it makes little sense to speak of progressive degrees of set-apart-ness. Rather it is progressive conformity to the image of perfect holiness, which is the righteousness of the most holy one, Christ.

2) about increasing "conformity to the image of Christ". What is it in us that is increasing? Is it something we can detect subjectively, like how in Wesleyan / Catholic traditions, it's the increase in virtues (as habits), or increase in character stability? If it is detectable and increasing/decreasing in us, isn't it infusion in reality?

We may with fallible estimation evaluate our progress in holiness, indeed, as Paul writes in 2 Corinthians 13:5, "Test yourselves to see if you are in the faith; examine yourselves!" and in Galatians 6:4, "But let each one test his own work". Holiness isn't really a thing that can be infused, it is just a declaration. Progressive holiness is just being continually and further conformed to Christ's righteousness, and we may evaluate this through comparison to what Scripture teaches. But we must recognize that our evaluation is not infallible, and that our progress is not permanent, we may go through seasons where we are less or even not at all conformed to Christ's righteousness before God calls us back onto the path toward conformity. I hope this answers your questions.