Reformation objections to lectio divina?

It is possible that the Reformers did not know about Lectio Divina. It had fallen out of disuse by the time of the Reformation. It has only been recently that the practice was revitalized.

Catholics have sacred scripture and sacred tradition which forms the magisterium -when a person believes they have received a private revelation of scripture while practicing lectio divina it can be confirmed or challenged by checking it against the magisterium, or it can also be checked against the catechism of the catholic church for a quick check--- a mystic is is one who has moved from a belief system or belonging system to an actual inner experience--- not to be feared

This subject is all about balance. Rationalism and Mysticism are the extremes to avoid. Your question does not seem biased to either extreme.

I do not think you will find reformers making direct attacks upon particular forms of meditation so long as those meditating, mediated on those objective doctrines that they taught! The moment any type of mysticism crept in that would give cause for someone to claim that their 'inner light' had authority over objective doctrine, they were called fanatics. Thomas Muntzer was a German reformer who went that way. Luther mentions his sentiments when discussing the necessity of the public reading of scripture:

First, attend to the public reading. Do not omit it. It seems to me that there is a miraculous spirit in those fanatics. Thomas [Müntzer] began it. So they hold the Word in contempt. “The testimony in my inner being is enough for me.” (Luther's Works 28.329)

However the reformers were not rationalists, they felt until the Spirit opened up the objective doctrine you did not know what you ought:

Secondly, you should meditate, that is, not only in your heart, but also externally, by actually repeating and comparing oral speech and literal words of the book, reading and rereading them with diligent attention and reflection, so that you may see what the Holy Spirit means by them. And take care that you do not grow weary or think that you have done enough when you have read, heard, and spoken them once or twice, and that you then have complete understanding. You will never be a particularly good theologian if you do that, for you will be like untimely fruit which falls to the ground before it is haft ripe. (Luther's Works 34.386)

However, to reiterate, if one's meditation was not centered on objective truth, and most importantly objective truth of grace, as opposed to works, one's meditation was self-based and idolatry:

The highest forms of religion and holiness, and the most fervent forms of devotion of those who worship God without the Word and command of God, are idolatry. Thus under the papacy it was regarded as an act of the greatest spirituality when the monks sat in their cells and meditated about God and His works, or when their fervent devotions so inflamed them as they genuflected, prayed, and contemplated heavenly things that they wept for sheer pleasure and joy. There was no thinking here about women or about any other creature, but only about the Creator and His marvelous works. And yet this action, which reason regards as eminently spiritual, is a “work of the flesh” according to Paul. Thus every such form of religion, which worships God without His Word and command, is idolatry. The more spiritual and holy it appears to be, the more dangerous and destructive it is; for it deflects men from faith in Christ and causes them to rely on their own powers, works, and righteousness. (Luther's Works 27.87)

From all the references about prayer or meditation in Luther or Calvin that I have read, which is a fair sum, never will you find an encouragement to practice mysticism, nor is the subject important enough for their attention. So long as people held to the doctrines they preached, meditation styles just did not matter.