Just curious if there has been any talk of anyone converting or making HK G3 sized guns into 277 Fury?

Give the two variations of high vs Normal Pressure loads, that might introduce a variable for the HK Roller system, but for standard loads I'd be curious if there have been conversions ?

The first hurdle would be finding a chamber fluted barrel.

And next is working out the timing with the locking piece for the higher pressure.

Working out a LP wouldn't be my biggest concern. I'd start with a 36 since it's the smallest commercially available and look at pressure signs.  Then I'd make a 28 degree LP and check for function to determine which direction the shoulder needed to go.  The chamber fluting is the hold up on most experimentation with the platform.

But first I'd want to hear from someone smarter than me who did the math on the barrel chamber and trunnion that knows they can safely handle the increased pressure over  a prolonged period.

Bet the high pressure ammo will sling brass so hard it really would be deadly

I think the bolt thrust would be higher than 5.56 which HK barely got to work as I understand it.

5.56 should have lower bolt thrust than a .308.  5.56 is about the same pressure with a smaller head diameter.

7.62 is about 30% more than 5.56, .277 is about 30% more than 7.62.

Would be pretty cool but even if you could find a locking piece to handle it, I bet it would be a hell of a ride.

If the .277 is a NATO thing I'd be interested to see if other 308 guns in service would be converted  like the HK21

Potential problem I see is that in a gun not designed for the .277 is you are essentially firing what would be proof loads for that action on every shot.

I agree - and 80,000PSI range is incredible pressure for a firearm cartridge - I think the underlying logic is - push it to the max and then throw it away.  
I was interested to see if the system (or for that matter existing NATO 308 rifles) e.g Beretta BM59 could be reconfigured for the new round - e.g. utilize platforms in 308 to the new cartridge - rather than invent new guns, merely new locking systems (or gas in gas guns)  to improve increased pressure demands rather than build new designed guns from the ground up.

In reality - perhaps the cartridge was supposed to be a red hearing for Russian body armor and small arms industry to go back and overspend chasing a new paradigm.

One way to defeat an enemy is to outspend them or have them dilute spending across too many platforms.

After seeing the equipment Russia is fielding in Ukraine this has been my thought as well.  Seems like the need wasn't so urgent...

It really wouldn't change much, the russians would just claim their new body armor can stop it, and keep issuing SAPI's filled with sawdust and cardboard