I agree on the 1♠ rebid. For these cases (GF support in a minor, partner rebids NT so no 4SF available), I bid NMF (obtensibly with 5 cards in my major, then support the opener's minor, GF, retract promise about 5th card in major. in this case, I am stuck for a bid, though. But would have bid 2♣, 10+, the first round.