Our jobs typically entail importing 80 to 250 cubic yards of soil. So with wet ground, and that many passes, it’s more than a “simple raking” and tossing seed downThe OP is trying to eliminate the RAKING
I think the key is using a Harley rake
You can get a turbo turf or easy lawn hydroseeder reasonably cheap too
We use Finn but they’re pricey However WE do predominately topsoil seed work.
If your hydroseed work is limited to small or repair type work... I would suggest one of the jetted (cheaper) models