Varnish is a black art best left to the masters of the Caribbean.
No thoughts on six sides at once -- with
varnish patience is a virtue. Then again, you might try to support the boards with some 1x2s on edge and do one surface and all edges at once, let dry, sand, varnish the second surface, etc....
Buildup in the paper may be because you aren't letting it dry sufficiently.
I've been told by them that knows that a really good brush is critical. There are also techniques that border on black magic -- e.g. one Rastamon that did my companionway used to put the varnish in the frig for a few minutes before he applied it. My guess is that this was to slow down evaporation of solvents (?) allowing more time for the finish to "float". He also used to thin the first few coats to get good penetration of the wood and he claimed that six coats was the minimum needed for a good job.
Good luck. When it comes out well there's nothing like it!