There are a number of rechambers possible in .308" bore, but if it is a 10" barrel many of them will not be practical. The most obvious candidate is the .30 Herrett, which gives 150-250 fps increases with 110-150-grain bullets over the Whisper. I have a 10" barrel in each and both are moa accurate. The .30-30 is not a good choice in a 10" tube, it won't do much better than the Whisper ballistically but recoil and blast are rough.
In 14-15" barrels the .30-30 works much better, and I have a .300 Savage that is a great performer and the .30-40 Krag is possible. The .30-30IA and .309 JDJ are wildcats commonly used.
The Contender frame is not limited by chamber presures but rather by case head thrust. The larger the internal cross sectional area of the case, the less pressure it can handle. Rough guides:
.223 case.............55,000 psi
.30-30 case..........42,000 psi
.44 Magnum case..36,000 psi
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