Respond to asking bids!

A disaster from last week I want to share with you. Playing MOSCITO, the bidding starts:
1♦! - pass - 1♥! - 2♠
2NT - pass - 3♠ - pass
3NT - all pass

1♦ = 9-15HCP, 4+♥, can have longer m
1♥ = relay with invite or better hand
2NT shows stopper and maximum hand, probably pretty balanced

3NT down a few, 4♥ went only 1 down I think, but both contracts can be made if you find the stiff ♣K...

First of all, my hand:
♠ x
♥ Qxx
♦ QJxx
♣ AQ9xx
Partner blamed me for not bidding 3♥ instead of 3♠, to show a 3 card support. Imo he knows nothing about my hand, so he just has to respond to my question, "I'm the captain of this auction, I ask, you respond", end of story. What are the possible meanings for a 3♠ bid? I guess there's only one sensible one (since we're in a GF auction): asking for a double stopper. So bid 3NT with a double stopper, bid something else without it.

Now partner's hand:
♠ A9xx
♥ AKJxx
♦ x
♣ Jxx
Clearly no double stopper ♠, so a clear 4♥ response (maybe even 4♣!). Partner said he can't know that I have a 3 card support, but he doesn't need to know this to respond to the question. I know why I ask the question, he doesn't.

Perhaps you're interested why I don't find 3♥ a good bid. Well basicly, I think 3♥ should show a 4+ card ♥ with slam interest! With invite/GF hands 4+ card ♥ support and no slam interest we immediatly start with a 2♠ response, so what else can 3♥ be after such an auction? Opener probably has a 4-4M, so why search for a 5-3 fit if he can hardly have a 5 card ♥? The only thing that interests me is a double ♠ stopper, without it I'll signoff in 4♥ which I thought would be a 4-3 fit (which is pretty ok with singleton in the short hand).