Like everyone else, I don't like 2♠. Even playing strong jump shifts, you don't SJS just to show 13 high - you have to have a reason.
But I also agree with everyone else that 2NT is worse (even if it's forcing, very old-fashioned. That's not disparagement; I actually prefer that style to the "standard" invitational. Just much more common to see 3NT as "13-15 balanced").
1♠ is automatic here, and whatever way you game force next round. Any other call is giving the wrong picture to partner.
In 5cM systems, it is imperative that responder show a 4-card major if they have one. Frequently even if there's a longer minor (if playing 2/1 GF, "unless you have at least a game-forcing hand, and possibly even then"). The system will not work if you don't; you will miss good 4M games into 3NT with 10 of the last 8 tricks, you will miss major slams; all kinds of issues.
1m-2NT, even if it's game forcing, only works as well as it does because opener can rely on there not being a 4-4 major fit; the only hands the system has to deal with is when she's 5=6+, or 6=7.
However, that's not the entire reason for the result.
In order to understand why you were in 4♠ and the room was in 3NT we need to see your hand. "13 with AQx xxx in the minors" isn't enough - we need the full shape, and possibly even all cards. If you were 3=4=3=3, and raised partner's spades, I'd be right there with you - if you're playing strong jump shifts, it really shouldn't just be on HCP, it should promise 5 (or at worst 4=1=5=3 or the like where this is the way you show the slam try minor fit). And you were the only ones in the flat moysian, which I'm not surprised played just like notrump. If you were 4=3=3=3, then I'm still not surprised you're in spades, for the same reason as before, but auctions like Joe's, where we can offer 3NT as an option "I'm flat, you're flat, what do you think?" are possible.
I am surprised that everybody was in 3NT if you had a 4=4 spade fit - that would be very uncommon except at the highest levels, or in England (where the room is opening your hand a 12-14 1NT, and 4333 might well just not look for the major fit and just blast 3NT). So it wouldn't surprise me in the least that you raised spades on 3, thinking partner actually had a strong jump shift hand, and got stuck. But we don't know, because we only have a complete look at partner's hand.
What to open with 3=3 in the minors outside of NT range is a perennial question. "Standard" is "4=4 D, 3=3 C, and I don't care if it's AKJ 532" - again, because the system is designed around "this shape bids this" on the first round. Many are moving to "Clubs if balanced, even if 4=4=3=2 or 3=3=5=2" - but they change their systems to handle that (and to take advantage of "1&diamonds; is almost always 5+, unbalanced"). Irrelevant for this hand, of course; it comes up more when the opponents overcall, or if partner is weak with "support". I try to minimize the number of hands where I end up playing a 4=3 diamond fit with two flat hands at the 3 level competing against their 4=4 major fit; I'll compete slightly less aggressively if my "fit" is clubs, because 3 is (much) more likely.
I haven't played Goren seriously - even 40 years ago when I started we had moved to 5cM. But I have played a 4 card major system, and one that strained to open the major for its preemptive value; so I can see that responder's hand might be a game-forcing 2NT call: "you didn't open 1♠, you don't have 4 spades". But in 5-card major systems, bypassing spades is unforgivable, especially with a weak doubleton (even in opener's suit, that's called "ruffing value").