We slow down for the offseason as well (only take 3 sims for the offseason vs only 1 for the regular season)
In all seriousness though, re-negotiations really only need 1 sim after the postseason to happen along with picking up or turning down of team options after the playoffs are over. Teams run the risk already of not having enough time before free agency at that point anyways.
Realistically you can just do one free agency period between the start of free agency and the rule 5 draft as well. Immediately after the rule 5 draft is the biggest judgement call depending on your league and its members to what would be best. Since free agency activity is the highest at the end of November and the first three weeks of December, You want to set a pace there that works best for your league.
Once you hit January and on, things kind of die down until you get to spring training really to the point where you really want to speed it up just to get things over with in my experience.