1H-3H: invitational vs. preemptive? How much does that change your call as the opponent?

In the swiss team game at the Macon sectional with both sides vulnerable, I picked up:
AKTxx
X
X
AQTxxx

It was 1H-P-3H to me. Your call. I bid 4C. I asked and the opener said 3H was a limit raise. So I thought they probably would bid 4H and then I can bid 4S and give a very good description of this hand. It goes all pass and dummy hits with soome 10 or 11 count and 4 spades to the Q, making 5C or 5S easily. After the hand, the 3H bidder said it was a preemptive bid, and their card agreed. So, I told the director that I would have made a stronger bid had I known rho was showing a weak hand. Making game is much more likely with a preempt instead of a limit raise on my right. So, what do you bid over 3H: 3S, 4C, 4H, or X? The director allowed me to bid 3S and partner raise to 4S, making 5 for a push instead of -10 imps. Fair adjustment, I think, and so did everyone else at the table, but I was beginning to reconsider it. Does the knowledge of rho's strength really change the way I bid this hand that much? What do you think? I actually think 4H is the right bid, whatever 3H means. This hand is strong and distributional enough to force to 4S or 5C.