Alternative for Rodinal
Glad you found a solution for your fogging; as noted, always first suspect your fixer.
As far as stand development is concerned, my own experience is a technique called "FFDD", or "Fast Film Diluted Developer". I used it extensively for theater and dance photography in the 80's.
Basics : take a normal, but vigorous working stock developer (like D-76), dilute it (e.g. 1 dev + 4 water), agitate for 30 - 45 secs, and let stand ; total dev time = original dev time (stock solution) x total dilution (here : x5)
Chemical/mechanical gist : fast film used to be thicker (Tri-X still is), and not agitating the soup made developer "exhaust" faster in the areas with more density (causing underdevelopment).
Result: "overdevelopment" of the areas with low density in the negative (the shadows in the original) without hiking up the gradation of the negative, but still gaining 2/3 - 1.5 stops in sensitivity (based on the actual sensitivity point).
Danger : bromide drag; you can see it as drag lines dropping down from your perforations on your neg, or as halo in dark areas (in the print) close to lighter areas. In theater photography (using 35 mm) some kind of halo above a character with a black background.
My experience indicates this can mostly be avoided if you agitate for 5 secs (1 up-and-down cycle with the tank) every 4' (on 1+3) to 6' (on 1+5).
The result is a neg that has a REAL increased sensitivity of 2/3 to 1.5 stops, without an un-printable contrast, but with a copy range of 8 - 11 stops (very useful in theater photography, but a PITA for normal lighting conditions).
A strong No-No would be the pre-soaking : this is useful when using very short dev times with a lot of agitation (used originally by press photogs to shorten their dev times), but when combined with stand development could lead to uneven development (you have to migrate your chemicals through a water soaked emulsion, not very efficient if you don't shake your soup constantly).
BTW, FFDD is bound not to be very useful on T-Max, because of the 2-layer construction, the thinner layers and less silver in the emulsion.
Of course, YMMV.
Wkr,
Geert