I've been noticing the same thing. At first I thought the random number generator was just unfavourable to me, but now I think that something's changed in the codebase...
I've gotten several cubimal boxes (all commons), several 100 currant wins and bunches of the 5c, 25c, and single bean - and do not remember a single music box or ticket from them.
I have seen very little from the tickets, especially recently. And that is since I have been actively working on getting icons. So I have been visiting the shrines regularly and not only do I not get very many tickets, when I do they are for 1 or 5 or maybe 25 beans. I cant remember the last time I got a musicblock, and have NEVER gotten anything more interesting-at least that I can remember. So can I donate the tickets? Maybe I will get more use out of them that way.
Or maybe I will experiment too and save them up and use a bunch all at once also. Will report findings if I do that.
Ticket issuance may be mood related? Just a thought. Maybe same for hand outs from the wheel, like with chickens, pigs, trees and rocks.
So best time to do them would be when you're über happy.
The pickings do seem pretty slim recently. Of course, I get so many music blocks from squeezing chickens that they're not exciting prizes anymore, which may have more to do with it. Never gotten a cubimal, which would be nice. Even if it was a common one, I could find an interesting place to hide it for someone to find. XD