I had a 7.7 Arisaka rechambered (not rebarreled) for 06 also. Mine shot .308 bullets very well in 150, 180, and 200gr bullets. It is my understanding that tolerances were not very tight, and barrel diameters were varied. Your might be a little bigger than mine if your rifling is in good condition.
Mine seemed to like the heavier loads better. I remember my brother getting a bear with a 200Gr Nosler Partition over 55gr IMR4350 and I took a deer with a 180gr Speer Mag Tip over 57gr of IMR4350.
Target loads were 147 FMJBT over 57 gr 4350, and they shot okay, not not nearly as tight as the others.