NavList:

Were gyrocompasses ever used for this purpose?  One could project a gyrocompass-referenced virtual marker onto the horizon (suitably far from the point below the Sun, say 90 degrees or so), then take distances to the Sun with a sextant to obtain the solar azimuth.  This would have to be pretty accurate to upgrade a conventional line of position to a fix, though (few arcminutes).

Cheers,
Peter

ps: after searching, I find this has already been suggested on NavList back in 2009 by George Huxtable:

http://fer3.com/arc/m2.aspx?i=108076&y=200904

Truly there is nothing new under the sun (pun intended).  So how good are gyrocompasses for accuracy, both modern ones and ones available in, say, 1930?