I occasionally use baclofen for this purpose. I either take 5 or 10 mg at bedtime when I do this. I'm also a nightly drinker, so I don't want to dose baclofen too high.
Baclofen is very short-acting. It may be (kind of) okay for inducing sleep, but certainly not staying asleep. Gabapentin would be far better as far as lesser-controlled GABA-B/adjacent substances go. Even tizanidine, clonidine's bastard cousin, would be better if alpha-2 adrenergic receptor agonists would be helpful. All purchasable. All I'll say.