Pglasgow
It is my thoughtthat if your Omega, with the laminate stock, is shooting well and shoots well across all conditions (heat - cold & etc) I would really leave it alone. A supported barrel, a barrel laying in the barrel channel correctly is better than a floating barrel - my belief...
On the other hand the synthetic stock could use some help. The Omega synthetic stock will probably function fine 90% of the time as is. If you float the barrel in this application by shimming you need to consider reinforcing the recoil lug cups. Currently the synthetc stock I have supports the barrel very well and the will shoot 1.5" groups most times... it will all the time - but i don't all the time.
Floating solves two problems, lesser quality stocks that have very flexible forearm that may change your POI - "floating" will cure that problem. 2) a stock that does not not apply equal pressure tp the barrel along the length of the barrel will cause POI movment as the barrel warms and cools, and again "floating" will heal that problem,
It is my opinion that most high dollar custom guns will have a supported barrel not a floated barrel. In the old days when Winchster built great guns they took the time to fit the stock to the barreled action - today that is to expensive to be competive.
Hope this makes some sense...
mike