Riles,

Your dropping pH is truly a mystery and it is true that in your case (and only in cases like yours where the pH is dropping consistently) a higher TA will help for multiple reasons. It will not only increase the buffering of the pH, but even more importantly it will increase the amount of outgassing of carbon dioxide which will make the pH rise. However, if you could hold off on raising the TA a few days until we figure out the mystery, that would be helpful because if we find the source we can turn it off and see if that helps. Otherwise, if you increase the TA to compensate it will be harder to isolate the source of the dropping pH (but it's up to you and I'll understand completely if you've just had it and want to fix the problem immediately).

I'm going to ask you some questions to see if we can figure out this mysterious source of dropping pH since it truly is quite strange given your source of chlorine.

Do you use a pool cover and if so, how often is it on?
Do you have any sources of aeration (waterfall, spillover, fountain, air jets, etc.)? I suspect not, given the pH dropping.
What other chemicals are you adding to the pool regularly (even weekly or bi-weekly) other than bleach (or chlorinating liquid) and Borax? Are you adding a non-chlorine shock (potassium monopersulfate) on a regular basis? Are you adding PolyQuat 60 or any other algaecide?
Do you have anything falling into your pool such as leaves or debris of any kind? If so, what is it that falls in?
Is there any runoff from nearby soil or is there liquid of any kind finding its way into your pool (other than what you explicitly add)?
Is there sunlight that shines on your pool?

As for your question about how to distribute Borax, I would just slowly pour it over a return in the deep end of the pool, but take a look and see if it seems to fully dissolve and not accumulate on the bottom at all. If it appears to be slow to dissolve, then I would mix it in a bucket first and then slowly pour that over the return instead. Try to pour away from the wall, if possible. These extra precautions are mostly due to your vinyl pool, though I doubt that the Borax will be a problem (it's not acidic and not chlorine -- those are probably bigger issues for vinyl pools).

Richard