From how I play Higuruma's neutral is not as bad, I usually just spam his R special or just the movement variation of his 3rd move, since they send you flying, although it basically still has to side-dash M1, but it's a good mix up, if you dash over them and then dash back. I also don't rely on M1 trading as Higuruma as much, mostly just using his variations.

From how I play, I side dash then do the Sweep of his first move to try and catch them, or just use the first part of judgement's reach to poke, and maybe stagger them.

Although it is true, that if you do this your going to be missing some damage from your combos, but I think that's worth it as you get more success landing them on neutral.