I have intimate carnal knowledge of the situation, both the OP's and my own.
In summary, and for future reference, I tracked mine down to the flare tailpiece adapter on the shank, and recommended to the OP to go to a 1/4" barbed tailpiece/faucet connection. I haven't heard his results, but it solved mine.
Also, for normal beer pressures and unstratified/even keezer temps (especially temps <35F), none of the issues regarding this situation causes any problems. For problematic situations however- like high carb/temps, short lines, etc.; having as clean (same ID) and as few transitions as possible can help.
Here is the short version:
I had a very similar setup, except for pouring through a 3/16 chrome shank and rear seal faucet using a barbed tailpiece. I was able to get decent pours, especially considering the carb level. Pours were mostly liquid with enough carb left for it fizz/explode on your tongue like champagne.
Looking to upgrade, I swapped out the chrome shank/faucet with a 4" X 1/4" SS shank and a 525SS using a flare tailpiece and swivel nuts (which is what the OP uses). Same exact pouring issues as the OP's- 100% foam with the resulting liquid lacking any carb. This wasn't temp related, as it occurred after multiple pours, and even when I left the faucet inside a non-collared chest freezer at 32F.
After lots of swapping parts and pieces, I narrowed it down to the flare tailpiece- either as the sole culprit, or due to the additional connection caused by the swivel nut that must be used with it. Either way, switching to the simpler 1/4" barbed tailpiece solved the issue.
And the long version (for the doubters/scientific types, and people from Missouri):
The 4" shank I used was the standard shank available at LHBS with the usual crappy bore machining. Thinking the roughness of the bore was the issue, I swapped it out for a slightly better machined Perlick 6" X 1/4 shank (though it is still not a clean bore). No change in the pour, still all foam.
I tried all kinds of combinations from my stash of old pre-mix soda fittings- 3/16" barb swivel nuts, 1/8" barb swivel nuts, and even a QD with a 1/8" output hole. (Most of this stuff is out of production now, I think.) Same results- all foam.
I thought maybe the shank diameter to line diameter abrupt change, or maybe the 525ss was the issue since it has the large open cavity with no internal shuttle to fill the space like on the 425SS and rear sealing faucets. So, I went back to the old 3/16" chrome faucet/shank/barbed tailpiece combo to get a baseline, and all worked fine again.
I then put the 525ss on the 3/16" shank combo, and it poured fine. That narrowed down the problem, so I swapped out the chrome shank for the 6" shank, and the pour was the same or better than the 3/16" X 4" chrome one. This pointed to the flare tailpiece or swivel nut flare fitting, or both, as the culprit. There is currently no way to test whether it is the adapter vs. the swivel nut, or both, since there is only one model of flare tailpiece available and you have to use both together.
Looking inside the flare adapter, though, it isn't too hard blame this as the offending component. There are a few abrupt steps and cavities in the inner bore. It also has a fairly large bore on the flange side. This works as a funnel when used on a Sanke keg coupler (as designed) to reduce it to beer line, but when used on a shank it causes a small-big-small transition from beer line to adapter to shank. This may be inducing turbulence and causing the foaming, or it could be all the steps/cavities.
I should have tried the flare tailpiece on the original chrome shank to double check things, but didn't feel like having to fit the 3/16" hard beer line onto a swivel nut for verification, then back onto a barb tailpiece to be able to pour again. I wish I would have put the chrome shank/faucet on the flare tailpiece early on, as that would have sussed out the offender more quickly. I think I may have even done that, but had too many sample pours by then.
For regular beers, the flare tailpiece used on a shank doesn't seem to be an issue, but for highly carb'd stuff it seems to cause issues. It would make sense that a barb tailpiece would work better, not just because it eliminates the flare adapter and its ID steps and cavities, but also since there is one less transition with the elimination of the swivel nut. The elimination of transitions is also a reason to use 1/4" barbs for the 3/16 bev-seal line (or vinyl line), even if it is difficult to get on. The ID of the 1/4" fittings is very close to 3/16", so you get a smooth transition when the line is swaged to fit over it.