Ok, so here's a hypothetical way do it that works without any pitch references and is in principle exact, assuming a guitar that behaves ideally (neglecting inharmonicity, which is really quite uncautious for plucked string instruments) and only needing some timing reference.
What you do is, you first tune the guitar to Pythagorean tuning. That works the way you described, by matching 3rd to 4th harmonics of neighbouring strings E to g. Then you tune the b string to a perfect twelfth (3rd harmonic) above the E string.
Now at this point you may think the guitar is in (relative) tune, and therefore there should be a major third between the g and b string. But it's not, actually! Not what we normally call a consonant major third. Rather, it's a Pythagorean third, with frequency ratio 81:64, while a just-intonation third has ratio 5:4 = 80:64 (a 12-edo major third lies right between these two variants).
That ratio 81:80 is called syntonic comma; it's a small-ish but significant discrepancy between tuning systems. Small enough at any rate that the comparison of both tones yields a beat with frequency you can literally count: you generate the just-intonation third (+two octaves) above the g-string, realised as the string's fifth harmonic (over the 4th fret). This you compare with the Pythagorean third in the same octave, which you find as the 4th harmonic on the b string.
Let's compare the ideal frequencies of both these tones. Starting from a440, we have 110 Hz for the open A string,
- so 3/4 of that for the E string, times 3 for the b string, times 4 for the harmonic you play thereon. the 4s cancel, we end up with exactly 990 Hz.
- 4/3 of that for the d string, again 4/3 for the g string, then fifth harmonic. 110 Hz × 42/32 × 5 comes out as 977.77... Hz.
So for ideal conditions, our beat frequency should be the difference of 12.22 Hz – scaling up linearly with the absolute tuning reference, so if we adjust that until it comes out with that frequency, we'd theoretically proven a perfect 440 Hz concert pitch.
How about practice?
Turns out this really doesn't work very well, mainly because the strings do have considerable different inharmonicity, and because those high flageolett notes decay too fast for counting enough beats to get the statistical errors reasonably low. 12.22 is triplets on tempo 244, but if I try the on my classical guitar the beat comes out more as quavers in that tempo – meaning, the error actually is something like a fifth!
So, this this definitely won't help you getting closer than within a semitone, but IMO it's still an interesting idea to consider.