Back to thinking about Kaplanville.

If 2H is a Fantoni-Nunes type bid, covering 10-13 with 6Hs or 5Hs with shape (but not including 4Ss), then 1H-1S(like a forcing NT)--1NT can cover the rest of the 10-13s with 5Hs. With a 5-4-3-1 one can decide whether to open 1H and rebid 1NT, or open 2H - in particular with 3Ss, one should open 1H to find a 5-3 S fit., and if 1S then open 2H to try to block a S overcall, since 2S by opps over 2H requires more values than 1S over 1H.

So 1H-1S--?

1NT: 11-14 not too shapely, not 4Ss, not good 14, could be 5-4-3-1 with 3Ss
2C: 13/14+, with a four card or longer minor, if less than 17 exactly 4 in minor and 5Hs
2D: 6+Hs
2H: 5Hs, 4Ss, up to 15
2S: 5H, 4Ss, 15/16-18, or 6-5+ in majors up to 16
3m: 14-16, 5-5+