I tend focus on taking pieces for a single puzzle via tags once its halfway complete. I know its random - but the odds are probably better that I won't get a duplucate when buying pieces if I am not sitting on a bunch of puzzles that are mostly finished. I will skip the pink pieces if I'm less than 10 pieces away from completing a puzzle.
That is the logical way to go for the puzzles that are almost done, and I plan to go that way once my pinks are finished. But I can't but want to grab them while I can since its the only way to get them. Plus, at this point, a good portion of my passes don't even have pinks these days so I'm still back to filling in the mostly full puzzles.
When progressing through the game the enemy armies are scaled in proportion to yours as of the first time you challenged them, so unless you lose there should never be an unwinnable matchup. It's actually favorable to keep your army size at a minimum until you complete the 2.9 runs needed for all the progression-based plaza tickets as it makes recovery from losses easier (assuming you don't do any force exiting before the game saves; and you can't do that twice in a row without forcing an automatic troop loss anyway).
Blech, I heard about that awhile back too. so that means that it's actually more to my benefit to check passes more frequently then for this particular game. Which sucks because for games like Find Mii and Mii Force it's usually more to your advantage to get your fights done in batches (more teamup opportunities, less anti-spell potion usage, some spells get better mileage like purple poison and pink criticals).
On a slightly different note, I need to figure out a decent 5 dollar game to get with the remainder of my card points. Any suggestions of good dsiware/3dsware stuff that's on the cheap?