First pick a COAL that will allow all cartridges at that nominal length to easily chamber in all of the firearms you will be shooting those reloads in. Bullet length and seating depth isn't going to be exact so you want something that is short enough to fit, minus at least another 0.005-0.010" fudge factor.
Then load a ladder starting low and working up. I typically don't start at the min load because that doesn't always reliably cycle semi autos.
I usually do max minus 8-10%. I'll load at least 5 rounds for each gun I want to test function in. Shoot the workups starting from lowest to highest charge. Look for the range that gives you the desired characteristics most important to you( function, accuracy, recoil, velocity, cleanliness, etc.) Continue your load development focusing more in on that range.
If you want bullets that are more exact in their weight, you need to buy better bullets. Hornady and RMR are good choices. That said, I really don't think the difference you're seeing is going to cause any issue. If you had a 125 gr. Bullet that you couldn't find data for, you would be using 124 gr. data to base your workups off of anyway.