Hi, congrats on a new (to you) rifle!
It is tough to diagnose a performance problem from one range session, but I always look at the action bolts' torque early in the process.  On my T3 hunter 30-06 with wood stock, I torque the bolts to 35-40 in-lbs.  On my T3 Sporter (laminated stock) .223, the torque doesn't seem to matter much although I tighten both bolts (front & rear)to same specs.

Floating the barrel should not cause problems, in fact the barrel should've already been floated unless this is an unfamiliar (to me)model variant.

Shoot more and different ammo.  I'm sure you have by now. How did it turn out?

You might also check for wear on the recoil lug. A bad fit there can affect accuracy as well. Depending on how many rounds it had through it before you got it, it may be time for a replacement.

Still looking for more information, but I doubt the recoil lug is the problem.  Did you torque the bolts properly?

I don't have a 22-250…BUT

My 223 gave the same results shooting the same Winchester ammo in 55gr…was disappointed like you but it was the ammo not the rifle. It's crap ammo for my Tikka's, none of my rifles shoot it well, it groups all over the place.  Nosler & Hornady shoot equally well for tight groups. 
Its not uncommon for the sporter barrel to throw a flyer if too hot…you have to fire 3 shots as fast as you can before the barrel heats up, or wait and fire each shot with similar barrel heat.  I usually get the same results with either method.

Switch ammo and give us a range report running some Hornady…Nosler… or any another decent brand through the gun. It will produce better groups immediately…if you get the same results its 1 of 3 things…the gun, the scope, or the guy holding the gun.  It usually isn't the gun ;D