It sounds like, as your rifle's barrel heats up due to being fired, it begins to bind against the forearm... and this changes the bullet's point of impact.
The more you shoot the rifle, the hotter the barrel gets, the more the barrel binds on the forearm wood and the more the bullet's point of impact changes. You proved this is the problem by removing the forearm... and once it was removed, the point of impact stopped changing.
The "fix" is to relieve the pressure at the point(s) where the warm/hot barrel is binding against the wood of the forearm as the barrel heats up. This is done by sanding the wood in the forearm's barrel channel away, using fine sandpaper wrapped around a round piece of wood of an appropriate size, until the warm/hot barrel no longer binds against the wood. It will then be necessary to seal the raw wood with a recognized sealing agent of your choice.
A good gunsmith can do this for you... or you can do it for yourself. BE CAREFUL NOT TO OVERDO THE SANDING if you do it yourself.
The Model 99 action is a very strong action and should easily withstand any "high energy" or "light magnum" type loads from Federal or Hornady. However, it sounds like you might have a rough chamber due to a lack of proper care by a former owner.
This problem can be checked out and, if required, easily rectified by a qualified gunsmith who will probably find it necessary to polish & smooth up the inside of the chamber. The point is to POLISH the inside of the chamber without increasing it's size. A qualified gunsmith will understand this and do the job properly.
Once these two relatively minor problems are solved, your Model 99 should shoot quite well.
My own 1953 Model 99 "EG" in .300 Savage (the cartridge from which the .308 Win. was developed) consistently shoots maximum loads consisting of 41.5 grains of IMR4895 behind a 150 grain Nosler Ballistic Tip bullets and sparked by a standard Winchester large rifle primer in once-fired Winchester cases into 3/4 of an inch at 100 yards. The chronographed muzzle velocity of this load averages 2680 fps... and it is undoubtedly close to or at the SAMMI's Average Pressure for a .300 Savage cartridge which is 46,000 C.U.P. ("Copper Units of Pressure").
The .308 Winchester cartridges is loaded to a higher chamber pressure (about 52,000 C.U.P.) and your rifle is designed to withstand the chamber pressure generated by the SAMMI Average Pressure for a .308 Winchester cartridge... the caliber for which it was originally chambered.
Therefore, the use of Federal's "High Energy" or Hornady's "Light Magnum" cartridges should not cause any extraction problems if your rifle's chamber is as smooth as it should be.
Don't give up on your Model 99... it's one of the strongest, finest and most accurate rifles you could own. :-)
Strength & Honor...
Ron T.
