Isaac:  I'm not sure I would do anything in your case 1/2 " after a lengthy cooling is pretty good   Anytime you switch something going from pressure bedded to free floated you run the risk of things not working as you hoped.  In other words instant gratifaction may not happen and a lot of extra load work-up can be needed.  Sometimes you luck out, but I find that unusual.  This is one of the reason I don't agree with letting a barrel cool between shots.  Normally what I do testing  after fouling shots is fire 5 round groups one shot after another then stop and let it cool to the touch and shoot another test load and repeat .  This will tell me more about a rifle than letting it cool between shots. Â
What size groups are you getting when you don't let the barrel cool , one shot right after the other ? Â If it's 1 1/2 " Â that's acceptable for a scoped std hunting rifle , Â 1 " is pretty darn good , 3/4" is really good and 1/2" is exceptional, Â those are the standards I strive to attain, doesn't mean I get there with all rifles easily. Â
I've seen it to where the shots may be stringing vertical, Â at an angle, Â or worst case horizontal , Â I might raise an eyebrow, but the groups are still within acceptable sizes. Â At least it's telling me down the road if I choose what needs to be done. Â Let's face it some rifles will never cluster in one ragged hole. Â
A good friend of mine awhile back got drawn for antelope here which is an extremely hard tag to get, Â and decided his 7mm rem mag wasn't good enough and decided to free float, bad mistake, it was throwing bullets all over the place. Â Crisis management set's in and nothing he did worked to get the rifle shooting until he put one of those donuts on the barrel. Â My point is be careful for what you ask for, and you don't have the time to correct it.
I do agree with Duby for lack of a better word gripping the stock and having forend movement. Â I think that can be very true under certain conditions. Â Very small free floating gaps in the barrel channel, Â very lite forend contours, crappy stock, being ham handed with a lot of pressure, use of non swivel head bi-pods I see it a lot (not so much on a bench , but when shifting the rifle around sideways), actions bedded only and no bedding forward 3 or 4 inches into the barrel channel. Â That just shortens up the overall length the forend has to move and makes it stiffer.
I know guy's are going to cringe when I say this the more barrel channel gap when free floating the better  within reason.  More air gap for cooling, less chance of stock movement and touching when you get a little agressive with the stock.  IMO 1/32 isn't enough, 1/16 may not be adaquate with certain stocks.  I've taken them to 1/8"  but only on rifles with enough stock to play with and not look ugly.  Although I wouldn't do that on any fine grade rifle and expect it to look the same . Â
If you are going to take the time to bed a rifle just do it right. Â Use a bedding compound that has very little give. Â Pillar bed the action screws if the stock is questionable for crushing which means most wood stocks and crappy plastics. Â Pillar bedding is nothing new it's been done for a hundred years + on wooden stocked military bolt actions. Â