Canape Transfers with Both Majors Invitational

One auction seems troubling to me:

1NT-2D
2H-2S

I play this as game invitational.  But, this auction seems troubling because the chances of a 4-4 spade fit seem lower than the chances of the 5-3 or better heart fit.  So, you end up in 3H a lot more than in 2S, it seems.

So, let's suppose that this auction is a canape sequence.  In other words, if Responder bids this way, he has four hearts and five (or more) spades, invitational.

The benefit is that pass happens more often, allowing the two-level stop more often.  That seems good.

One objection might be that Opener could super-accept hearts, the four-card suit.  So?  If you have invitational values and partner super-accepts your four-card heart suit, this is a good thing!  Not only do you simply bid game, but the opponents have no idea about the side spade suit trick source.

The corollary to this is that you now need to handle the invitational hand with four spades and five hearts differently.  OK -- same deal.  Transfer to spades and then bid three hearts.  Again, passing occurs more often, even if this gains nothing really.  But, you get that added benefit of the super-accept non-disclosure.

And, the benefit of this super-accept is not without substance.  Whereas most super-accepts occur in the context of a 9-card fit, these super-accepts will occur a tad more often, because only a four-card fit is needed to induce the call.  So, the non-disclosure will probably occur quite frequently.

Transfers, then, would show five or more of the major OR four cards if invitational values and both majors.