So my fears were confirmed. 3DS sound is not good for relay.
I need to do a little more test but it seems if you're playing an MP3 the internet functions cease to work, meaning no relay possible. Regular streetpass still works though. If 3DS sound is open but you've not started to plan an MP3 the relay still seems to work.
Makes me wonder if some games behave like this too.
Its just something to bear in mind if relays have not worked well for you (yes, I do use the 3DS as an MP3 player, in particular on train journeys*).
Also I got two first streetpasses in a row (as in both Miis were 1 plaza 0 hits). Plus one of them had the piece I needed to finish the Kirby puzzle panel (Super Mario galaxy 2 is my only 15 piece one left, the 24 piece puzzles are more complete than it though).
*-Guess I need to add that to the routine, when train stops at platform, hit home button (assuming Nintendo zone from whatever cafe is connectible from the train).
and gold chests are near impossible to get unless you happen on an exact large piece to perfectly complete an large room.
3*4 gives me some success with Gold chests (in the 0-2 range really depending on if storage rooms or Miis mess that up). Filling in the 2 in the middle is not too hard (as there is only one possible 2 piece). 3*5 is not too bad odds-wise either.
If you ever find the paint pot item it might be worth keeping in your inventory if you want to go for a super large room (outline then when the piece to fill it comes you can change it to be the right colour).
There is a bit of luck between setting up rooms on suitable floors (and the random initial placement* on floors being good colours) and finding the stairs. Then there is the what colours do I rarely streetpass (assume play coin colours are even), in my case Green, Orange, Pink are very rare but blue is common.
*-The placement is the same for all players, its the colours that are not.