I picked up a team last season that sounds similar to yours. Obviously you don’t cut anyone until Jan. 31st because one man’s garbage is another man’s treasure. I was surprised how many marginal guys I was able to move in about 6 off season trades. Don’t be surprised if other teams come at you.
Second, be willing to take on salary even for slightly overpriced guys. I tabbed several high priced guys coming off mediocre or underpeformed years: Rendon, Greinke, Schoop, Posey, and then nabbed Harper on 1/30.
If you accept reasonable trades, you’ll gain the reputation of being someone who accepts reasonable trades and other offers will come.
EDIT: After tradeing for the above mentioned guys, I kept 15 players and went into the auction with $190 to spend. Finished 2nd in the league.