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(1y) 1NT

I suggest playing Gladiator at (1M) 1NT, which is more effective against a major suit opening, especially 1♠. Aggressor can have 5 hearts at (1♠) 1NT because 2♥ would be an underbid. We get an additional cuebid to invite with 3 hearts, roughly equivalent to Puppet Stayman. There is also an indirect 3NT for choice of games with 3 hearts.

This version of Gladiator originates from a BTU gadget.

(1♠) 1NT

(1♠) 1NT -
2♣!(R), Gladiator
2♦♥INV, 5+#
2♠!STAY, INV+, 4=♥
2♠ - 3♠!COG, e.g. MAX 3433
2NT!NF INV, 5+♣
3xFG, 5+#
3♠!SPL, 0–1♠, 4=♥
4♣♦!Leaping Michaels, 5+♥, usually 5+#
4♥S/O, 6+♥
4♠!Leaping Michaels, 5+♦, 5+♣
(1♠) 1NT - 2♣
-
2♦!P/C
2♥!P/C, 5+♦
2♠!MAX, 4=♥, 4+♦
(1♠) 1NT - 2♣
- 2♦ -
PS/O, 5+♦
2♥S/O, 5+♥
2♠!INV, 3=♥
2NTBAL INV
3♣S/O, 6+♣
3♦♥INV, 6+#
3♠!SPL, 0–1♠, 0–3♥
3NT!COG, 3=♥

Slow 3NT still has 3=♥ if the right-hand opponent bids up to 2NT.

(1♠) 1NT (2♣♦♥♠)
2NT!TRF LEB
3♣!TRF INV+, 5+♦
3♦!TRF INV+, 5+♥
3♥!FG STAY, 4=♥
3♠!SPL, 0–1♠, 4=♥
(1♠) 1NT (2♣♦♥♠) 2NT
-
3♣!P/C
3♣ - 3♠!SPL, 0–1♠, 0–3♥
3♣ - 3NT!COG, 3=♥
3♦!P/C, 5+♣
3♥!P/C, MAX, 4+♦, 4+♣
(1♠) 1NT (2NT) -
(3♠) - -
XPEN, 3=♥
3NT!COG, 3=♥

I have not yet come up with how we utilize the slow cuebid.

(1♥) 1NT

(1♥) 1NT -
2♣!(R), Gladiator
2♦♠INV, 5+#
2♥!STAY, INV+, 4=♠
2♥ - 3♥!COG, e.g. MAX 4333
2NT!NF INV, 5+♣
3xFG, 5+#
3♥!SPL, 0–1♥, 4=♠
4♣♦!Leaping Michaels, 5+♠, usually 5+#
4♥!Leaping Michaels, 5+♦, 5+♣
4♠S/O, 6+♠
(1♥) 1NT - 2♣
-
2♦!P/C
2♥!P/C, 5+♦
2♠!P/C, MAX, 4=♠, 4+♦
(1♥) 1NT - 2♣
- 2♦ -
PS/O, 5+♦
2♠!S/O, 5+♠
2NTBAL INV
3♣S/O, 6+♣
3♦♠INV, 6+#
3♥!SPL, 0–1♥, 0–3♠

(1♣♦) 1NT

Otherwise, I suggest ignoring the minor suit opening. Take the 1NT overcall as a strong notrump opening.