Testing, testing...

[stanc]

Take the 120 GMX shape, use voids up front to move the CG aft, different materials for improving penetration, etc., to reduce the weight to 100 gr and one gets a BC of .400 assuming the same shape factor.

The bullet would have 90% of the sectional density of the M80, so would need some design effort (e. g., M855A1) to bring the barrier defeat and armor penetration up to the M80 level.

Using a void up front may be an option for the UK and Europe, but it's likely a no-go for the US Army, which seems pretty well locked into the exposed penetrator design of M855A1 and M80A1.

I don't know what different materials you're referring to. The only viable choices seem to be steel and copper. NAMMO's lead-free bullet is an FMJ with steel/steel core, and the RUAG projectile (like the US bullets) is steel/copper.

If I figured correctly, scale down the 130gr and 149gr versions of M80A1 to 7mm, and the resulting bullet weights are 101gr and 115gr, respectively. 6.8mm and 6.5mm versions are much lighter, IMO far too light to have a chance of achieving the necessary terminal performance.