Learn English – unconventional structuring of sentences

There are sentences that start with "for verbing" but that one isn't a particularly good one:

For eating right away, I prefer Macintosh apples.

For fitting into a small space, the Smart Car is terrific.

For educating children, schools are the usual solution.

So if your question is "can I do this?" the answer is yes. If your question is something else ("What is this called?" "Is there generally a better way to word these sentences?" "Is my particular example grammatical?") then I suggest you edit the question to include an actual question.

What is at issue, I take it, is whether "even though" can be in construction with a following root sentence, or whether, on the other hand, only an ordinary sentence can be in construction with "even though". The category of root sentence was introduced into modern grammar by Joseph Emonds -- this is a sentence which occurs only independently and not as part of another construction. (Well, that's not the whole story -- root sentences can occur as part of a few other constructions.) Fronting the adverb in your unacceptable examples is possible only in a root sentence, and this is why the sentence with the fronted adverb, since it is a root sentence, cannot occur as complement to "even though", because then it would be part of another grammatical construction.