I sanded with 60 grit and I came across a similar type of problem. I had to brush on the poly, it took a while.
There's nothing wrong with a good thick coat of poly... you haven't screwed anything up too much yet and you shouldn't feel bad for having attempted something a bit unorthodox in order to receive what you perceived as a better result. If it weren't for this line of thinking, we'd still be in the stone age. (seriously, someone thought that combining copper with another metal may make a better metal, hence bronze)
What you may consider doing is sanding the poly though... maybe with
150 grit... just a quick once over to knock down the tough spots. This will leave a 'white" finish, but don't worry...as soon as you apply the next coat of poly it will make it clear again. Try in a small area if you don't believe me.
If you apply too thick a layer of poly, you can get "orange peel" texture...which kinda looks lousy, but it does have considerable more traction when wet! you can sand orange peeling in poly down with 150 grit very very easily and it will look super neato when you're done.
If you've got any lamb's wool stuck in the poly, you may have to knife and plier it out. I had an issue with hair like that once. Who would've thought there would be that much hair in a house! Gosh.
Oh, it's gonna take forever to dry. I use Minwax fast-drying poly, and it takes overnight just to get tacky then by about the next night it's semi dry. NEVER EVER sand poly that hasn't completely dried. When poly (or any other oil-based finish) dries it exhibits an endothermic reaction, this means that as the molecules strengthen their bond they produce heat and when it's flat on a surface the heat's got plenty of place to go without buildup, but if you sand a floor and all those little pieces or poly are piled up, the increased surface area will cause much more heat much more quickly and it won't have much place to go...leading to a flame!
Take your sanding dust outside, put it on concrete or soemthing to dry. DO NOT pile it up, and never ever leave your sander's dust catcher full of the stuff, or the floor you just finished will just become kindling.
good luck!