.003" is less than the thickness of a piece of paper.
I'd think you could get more radial expansion than that due to the barrel heating up.
Too close IMO.
There is one way to find out if this is true..
The orgional poster here should take his rifle and the feeler gauges to the range and fire 5 or 6 quick shots on a warm day.
That should be about as many shots as one would expect to fire with that rifle under any big game hunting conditions and would be about as warm as that barrel would ever get.
If a .001' or thicker feeler gauge will pass with the barrel that hot, I'd say it's good to go.