you can seed with a cold weather rye now and it will germ - any northern blend annual rye will do
in addition to staking down bales of straw, spread loose straw on the soft spots and work it into the top layer of soft soil with an atv, tractor, etc.

some of those spots look like they will always be painpoints, you might want to look into some rock and geotex/burlap


Mat Peirce
1.25 acre southeast Iowa pond
LMB, BG, YP, WE, HSB, RES, BCP