If you can use a hydrometer in a sanitary manner, you’re equipped to spund in your serving keg.
Pull a sample 24 hours into ferment, hold it warmer to make it ferment faster, and that will give your FG.
Then transfer your beer to the keg when it has about 4 gravity points left. It will carbonate itself in a few days and be able to dispense at least half the keg, sometimes the whole thing, under its own pressure. (Flow control tap would be a big help).
How do you judge when you are 4 points from final gravity? I get that much swing on FG as a normal ending point.