I have a PTR 91 in 308 Win and it is a roller bolt like your Hk 770.
I am going to recommend either IMR 3031 or any of the 4895 series of powders, that is IMR 4895, H4895, or AA2495 powders, and 150 grain bullets. The 308 Win cartridge was developed in WW2 with IMR 4895 so that powder is pretty hard to beat performance wise, and pressure curve wise it is appropriate for your rifle. I would not use any powder slower than IMR 4064. I would use 42.5 grains IMR 4895 with a 150 grain bullet, that produces just at 2700 fps in my M1a's. I tested 41.0 grs IMR 3031 in my gas guns and bolt guns and 41.0 grains is a good load, just a little less than 2700 fps. IMR 3031 is a faster powder than IMR 4895 and that is actually all to the good in this mechanism. You want to residual breech pressure to drop quickly, especially in delayed blowback mechanisms. Current production IMR 3031 is short cut, which is great. The older stuff was as long as IMR 4064 and did not throw with a hoot. IMR 3031 is a pre WW2 powder and a really excellent powder if you are not trying to get magnum velocities.
I do not recommend any bullets heavier than 150 grains. The military round was a 150 grain, my PTR functions fine with bullets up to 174 grain, but it kicks more than I like, and I think it could be hard on the mechanism. There are lots of good 30 caliber 150 grain bullets, it is not like the bullet will bounce off the hide of animals.
If you reload, full length resize your cases for this rifle, do not think for a moment about "neck sizing" or "partial neck sizing". Considering neck sizing will stick cases in bolt guns, I am sure that it will stick cases in a gas gun. Buy Wilson type case gauges and size to gage minimum.
This rifle is a delayed blowback and for it to function, the gas has to be able to flow down the sides of the case and break the friction between case and chamber. This is not well understood in the shooting community, the leaders of the shooting community think that "increasing bolt thrust" is bad, and that really shows the lack of theoretical and historic knowledge about firearms, and the lack of gravitas in the leaders, and in the community as a whole. For this rifle, and every gas gun ever created, you want as little friction between the case and chamber as possible.
These flutes go down 2/3's of the case, the bottom 1/3 of the case provides the gas seal.
So, keep your chamber clean. Buy a 308 Win chamber brush and use that in keep the chamber clean. Dirty ammunition, ammunition with tar sealant around the bullet, will clog those flutes and gum up the mechanism. PTR used to maintain a list of dirty surplus ammunition that would clog up their rifles, I did not see it on their web site, so maybe all that surplus is gone, but regardless, the principal of using clean ammunition and keeping a clean chamber for a roller bolt has not changed.
You can reload cases fired in a roller bolt even though they look awful:
Don't forget to grease the heck out of the bolt and rollers!
The Swiss issue what appears to be a moly lube for their roller bolts, I use a light grease (lubriplate AA130 or equivalent) which I wiped off for the pictures, on the cocking piece, on the rollers, on the bolt head. Since the HK770 was last made in 1986, you don't want to create pre mature wear on the thing and try to find parts in the aftermarket.