Trophy Hunter XP 11 223 Help

Recently got a Trophy Hunter XP in 223. Didn't shoot great groups but initially just used bulk ammo so didn't think much of it. I didn't like the stock so I put a Boyd's Featherweight Thumbhole stock on.
I got some better ammo and the groups are no better 2-3 inches at 100 yards off a bench with front and rear sandbags. I am relatively new to shooting but I have a Savage FCP-K in 308 and shoot consistent 1" groups off the bench. Using a Nikon Monarch 4-16x42 scope

Read through the boards and tried some of the suggestions posted:

Made sure barrel is free floated - I am able to run a dollar bill entire length
Replaced scope mount and rings and torqued to specs
Made sure action screws torqued
Tried several different brands and weights of ammo (Hornady Steel Match 55, Ficochhi Sierra King 77 and 69, PPU Match, PMC)

I have seen some recommend to fee float the tang. How do I do this?

What else should I do?
Any and all suggestions appreciated?

Thanks,
Steve

What' the twist rate of the barrel? That will dictate which class of bullets you should start with....

Twist is 1:9. Savage recommends 69 grain and I have tried 55 to 77 without any improvement.

Have you ever cleaned it?

I would say the action should be pillared and bedded. To float the tang, the pillars should be tall enough to allow free floating the tang and still allow the mag to work. If the mag won't work because the pillars are too tall, shorten them, then grind down the wood beneath the tang so that there is enough clearance to allow a business card to be inserted all around it.