"...barrel is best if it's free floating?..." Nope. Only some rifles like a floated barrel. Some really hate it. The only way to find out if that particular rifles likes it or not is to try it. And it's not the entire barrel. Only from the chamber area forward is floated.
A great deal depends on where and how the thing is touching too. If it's over the whole length, that's rarely a good thing. Isn't good if it touches on one side only either. If it's just a tiny bit(inch or so) just aft of the end of the forestock, that's a pressure point.
However, floating a barrel guarantees nothing. Either way, you need to shoot the thing before you do anything.
The stock material matters as well. Wood that's not properly sealed(isn't expensive or difficult to do. Any wood sealer will do.) on the inside can and will swell to touch the barrel and alter the POI with humidity changes. Synthetics do not but can move if the screws aren't tight.