Love the swedes!
Curious how it shot before you began your efforts? These swedes tend to be awesome shooters, and I'm guessing you're only trying to get the most out of your rifle. When I try my hand at accurizing, I do it in steps, and compare progress.
Free floating shouldn't have any negative affect, and in some rifles a touch of upwards pressure can help, but to truly dial in your rifle, you'll want to compare as you go. Try it free-floating, then experiment with shims in your forestock(I've not encountered any swedes with this, but I've lived a sheltered life with too few 96s in it). Bedding is also another step that can be used with success.