Is the following rationale for sharing the gospel consistent with reformed theology?

Two aspects seem inadequately covered in the previous answers: the natural human response to good news (Gospel) and the glorification of a person one loves (particularly a hero).

One would think it odd if a citizen of Berlin did not become a bit evangelic about the fall of the Berlin wall but just went about as if nothing special had happened and when told about the good news of great joy just said something like "I already knew about this wonderful news and have already taken a piece of the wall. Now I need to get back to work." There is something human about wanting to share good news. (Of course, fear, doubt, and other factors can suppress this natural inclination.)

The motive of glorifying one's beloved is also a very natural, human motive. One might think it a bit odd if a husband did not want to tell the world about some great accomplishment of his wife (though this sort of boasting seems more common with parents and children). The husband would naturally try to convince others that the accomplish is great which includes expressing the relevance to each individual. This aspect may be expressed in 1 Peter 2:9b: "that you may declare the praises of him who called you out of darkness into his wonderful light" (NIV). Even Christ as a hero should naturally generate boasting (e.g., consider how some boast of the accomplishments of sports heroes; I suspect that such boasting would occur even if the boaster knew the other would never be convinced beyond "okay that person is not the worst athlete in the world").

Even if there was no love of neighbor, no awareness of the command, no appreciation of being an active part of this grand plan of redemption, I suspect basic human nature would provide some motivation for sharing this Good News; so part of the answer to "why evangelize" may be "because one is human" (the perfecting of this humanness may 'simply' be part of sanctification; so true humanness plus an awareness of the goodness of the news with a love/admiration of the hero behind the news would lead to spreading the news).

The problem you raise is only a problem because a doctrine has been cherry-picked and used out of context. Taken in step with and understanding of God's Covenant relationship with men and the whole counsel of Scripture, this becomes a non issue.

And no, your suggestions are not particularly in line with Reformed theology, at least not as a motivation for evangelism.

Frankly, those just are not the Biblical terms this issue is framed with (see warren's answer). The common responses that you listed as "not intellectually satisfactory" are likewise somewhat lackluster, and even concerning that intellectual satisfaction is being used as a measure of their usefulness. What happened to faith or obedience? Do you find the command 'thou shalt not murder' to be intellectually unsatisfactory? Is that even a valid question?

God commands it. If a direct order from the maker of heaven and earth isn't good enough rationale what is? But seriously, to somebody who has first received and been transformed by this Gospel the order to spread the message is hardly a burden or unsatisfactory assignment. What higher privilege could we be given than to be charged with such a task?

A proper understanding of predestination must be taken in the context of the whole of Scripture, from which we understand not just that God has chosen people, but HOW he works to bring those chosen people to himself. Through His word. How shall they believe if they have not heard? Who is charged will telling them? Who are we told to tell? Everyone.

Election is God's business, it says nothing about what man is going to be able to figure out about other men along the way. This quite has always amused me:

If God had put a stripe down the back of every one of his elect, I would walk around London lifting up coattails. Since God didn't, I preach "whosoever will." -- Charles Spurgeon

Election isn't something you see written on people's foreheads as you approach them with the Gospel. "Hey Sir can I tell you something? I've got this great news about a Savior. See, you're lost and ... wait let me see that ... sorry to bother you, this message isn't for you."

Has the Gospel done its work in you such that you love lost people the way Christ did? These kind of objections / sentiments seem to come mostly from people who have never actually reveled in the sheer magnificence of what they have heard nor shared that message and watched it do it's work in others. The Word changes people. Transforms them from dead bones to living beings. You watch this happen a time or two and the question "why share these words" stops even being a question.

Hyper-Calvinism is easily avoided by preaching the Word itself rather than Calvinism. The doctrinal framework may help us understand the word, but it itself is not the word.

If you really need a way to think about it, I was once encouraged by a preacher who used my sister as an object lesson. "It's obvious to me you love your sister very much", he said. "Now, what would you do if she was lost? She has been abducted and is a slave somewhere. Is there anywhere you wouldn't go to find her? Is there anything you would not do to win her back? Would any depth of she might have been plunged to ease your desire to reclaim her?". By the same token as adopted heirs of Christ, we have family out there that is lost. We don't know what they look like or where they are. We don't know what level of depravity they might have sunk to or under what guise they pass. What we do know (an these are Biblical terms) is that they are enslaved to sin, bound in darkness. Do we love them? If so are we still going to sit around looking for an intellectually satisfying reason to get out there and find them?

2 Corinthians 5:20 (ESV)
²⁰  Therefore, we are ambassadors for Christ, God making his appeal through us. We implore you on behalf of Christ, be reconciled to God.