I have a Weatherby Vanguard Stainless Synthetic in .243win.
I also free floated the barrel and the accuracy went down like a wrought iron hang glider.
I placed small shims between the forestock and the barrel made from a cut up plastic credit card/club membership card.
This improved my accuracy to about 0.5 MOA at 100 metres.
Having a couple of credit card shims placed under the barrel didn't look real great, so I removed them and replaced it with a small block of high density rubber. This was bought in the form of a sheet and cost about 2 bucks for a lot.
The block was approx 4-5mm length and width and approx 2.5mm in depth.
I used a small razor blade to cut a very shallow V shape into the block and placed this between the barrel and the stock. Its rock solid and does not move. The V helps the barrel to locate itself.
Now she shoots about 0.5 MOA again and does not have credit card bits sticking out of it.
I got the idea about the credit card shims from a Graybeard post some time ago. The rubber was my own brainbox thinkin. If I was half smart, I would know how to look for that post and and post it again...... Graybeard, if your listening?
good luck, keep us informed.