On a calm day, at say 200 or 300yds, start shooting slowly watching wind flags and mark on a piece of paper/target where every shot lands.
I put up 3 targets on the same level and shoot 5 rds at each target. watch where each shot lands and record.
If you take 15 shots on the same target, pretty soon shots overlap and get lost.
If your barrel warps, there will be no doubt that you start to see your group grow outside of the target center and elongate your group further and further away from center. Looks like a tail trailing off away from the center.
Or.... the group slowly gets larger and larger.
cool the barrel down, repeat. Odds are you will start to see the same pattern after the same number of shots.... problem identified. Decide if you can live and cope with that or not.
A problem you know, although not ideal, can be dealt with as long as the adjustments don't push you too far from center.
If you find that after 15rds, you can stay MOA'ish and this is repeatable, you have a decent enough barrel to let you learn how to read the wind. At this point, you say - 4 ring on target is my "5". 5 ring on target is my "V".
Essentially, you shoot on a TR target sizewise.
As long as your shots land in the 4 or better, you are shooting to the potential of the rifle and doping conditions well. In fact, if you never go outside a 4, you are shooting superbly and very competitive to your peers.
Know the potential of your gear and shoot to that potential. That is how you will learn and improve. We all want 1/4 min laser zappers but the budget to acquire and maintain may be beyond some at the start.
If you can dope conditions, each shot, every shot to the potential of your gear, you are actually shooting better then a lot of mega rifle shooters
Wind is everything in F class. Best gear to competitive may only vary by 1/3 min. How much we miss conditions can be measured in minutes sometimes.
Do not discount the Hrn 168gr BTHP or Amax. for the Rem, the Hrn 178gr amax might be ideal. These are much more affordable and for the barrel you are using, may not shoot any worst then Bergers.
Watch the flags and learn the mirage....Your rifle will get more accurate over time.
Enjoy...
Jerry