I think all 80 grainers would be fine and maybe some 90's too.
Hornady has a lot of nice 6mm bullets in the 50-80gr ranges, I might try their 87gr BTHP just to see, it looks a little shorter and might stabilize fine.
6mm/.243
- 8" Special for VLD bullets over 100 gr.
- 8"* Ratchet rifled 4 groove
- 10" For bullets up to 120 gr. and VLD under 100 gr.
- 12" for bullets up to 85gr.
- 13"* for bullets up to 75gr.
- 14"* for bullets up to 70gr.
- 14"* Ratchet rifled 4 groove
- 15"* Special for bullets up to 70gr.