First, I would try turning the carbonation down. You've got 5 psi needed to make up for the 10' of elevation gain, and 20' of 1/4" is going to take 17 psi (micromatic numbers) to overcome - if you set it to 22 psi at 40F it's going to be have about 3.4 volumes, too much for most beers.
If you are stuck with 20' of line, get something larger diameter. If you go to 5/16" hose, it will need ~8 psi instead, for a total of 13 psi. That's about 2.6 volumes, better but maybe still high. So think about 3/8" line, that will restrict it about 4 psi for a total of 9 psi which is 2.2 volumes at 40F. Much better. You could also go with an even larger ID hose and then go with short sections at the keg to add restriction to get the pour you want.
Finally, if your first pour is very foamy and subsequent ones get better, the system is probably too warm at the tap. That's a tough one to overcome without dropping some coin, but trunk line will help and there are cheaper ways to chill it than a glycol system. A bucket of water with a submersible pump will recirculate coolant through the glycol line - less than ideal, but better than nothing.
It's going to take some new fittings and some experimentation to get the pour you want, but this route will be way cheaper than trying to integrate nitrogen. The nitrogen systems are really only needed for long draw systems and pouring nitro beers. Your draw is not long enough to worry about that.