Howdy-
Using MAME 115, I got some pretty interesting results, using my mechanical rotary stick & my Ultimarc Rotary Joystick Interface (w/ new chip).
I agree that all the SNK games you list work, except TNK III is a bit flaky. It seems to have trouble at first but then it works OK. This is after just a few tests, nothing too rigorous or scientific, so don't take it as fact. I thought it might be a case of going into the settings & tickling it & coming back out of the settings until it worked, but just playing with the joystick for several seconds seems to make it work perfectly after letting it glitch for a bit...
I tried setting up Ikari 1 to work with a spinner, which required enabling my mouse. It works fine w/ a spinner, as long as you tune in the analog settings to your liking, but I don't like it. Definitely weird. I didn't go further with any other games--I don't know if I'd be OK w/ using an optical rotary stick, but using an optical rotary spinner knob is certainly whack.
Then I looked @ your "does NOT work" list:
Cal .50: my mechanical sticks work quite well w/ this game!!! I set up dial dec & dial inc to correspond to the mechanical rotary keys ([ & ]). Default settings are 15 & 15%. This is really close to working fine. Cal .50 guys seem to have 16 positions (verified by setting up the spinner & testing). I'm having a little trouble dialing in for 1 "click" to be exactly 1 rotational increment for my Cal .50 guy, but it's close. I either set it up so it occasionally doesn't index or occasionally moves 2 ticks when I rotate my stick. After much trial & error, the best I can do is 14 & 15%, a far cry from the 0 & 100% settings on the SNK games. Playable! Not perfect, but playable!
Downtown: works also. I found 38 & 38% to be a good setting that works pretty well. I didn't spend a lot of time tuning this in. I also learned that Downtown is lame & doesn't let you mess around for even a minute at the beginning to test your darn joysticks, as some of the other games do (Heavy Barrel is generous!). :\
Exterminator: works fine w/ defaults of 10 & 50%. This game is least affected by the inaccuracies of the sticks, because you can rotate only a limited angle before you hit a stop. And it's the only one that's not a top-down view, so it's less obvious if you're getting a 1-to-1 correspondance between your stick rotation & your character rotation. But, can I just say "WTF"!?!?

Gondomania: 15 & 100% work OK.
Heavy Barrel: Tip: Don't pick "Heated Barrel" from your game list. It's much less fun. Read carefully before selecting! 14 & 100% works well enough (not perfect).
Midnight Resistance: 13 & 90% is pretty good.
Time Soldiers: 13 & 100% is decent. This is a 12-position game, not 8, like most of the others.
General comments. It seems that you have to enable mouse in MAME to be able to use keys to do your rotating... Remember to deselect the analog input when you set up "Input (This Game)" (it's the entry right above the Dec & Inc in the list of commands for this game), so that you don't accidentally rotate your dude by tapping the trackball...hmmm, or this could be a planned sabotage tactic against your partner...

So, all in all, this works well enough for me--I'm not going optical. I've tried to make the settings a little "conservative" so that a rotational notch of the stick is more likely to *not* rotate your dude, rather than overrotate him. However, it appears to be inconsistent--with the same settings, sometimes a rotation click doesn't produce an on-screen dude rotation, but sometimes he'll go 2 notches. Close enough--just pretend you're playing on a beat up arcade machine! Faithful emulation!
I don't really understand the 2 settings great, so I welcome anybody to tweak these settings & post their results! SGT wrote up a nice summary of this in my previous thread on this topic:
http://forum.arcadecontrols.com/index.php?topic=81068.msg846063#msg846063Thanks,
-Jason
So I went through and tested all the rotary games to see which ones supported the 1-click/1-turn functionality by setting digital speed to 0 and the sensitivity to 100%. Maybe this is old news, but I couldn't find it anywhere else.
Using version .123 of MAME and my keyboard, it looks like all of the SNK games work properly, but none of the other games support it.
So it works in:
Bermuda Triangle
Guerilla War
Ikari III - The Rescue
Ikari Warriors
SAR - Search and Rescue
T.N.K. III
Victory Road
It does NOT work in:
Caliber 50
Down Town
Exterminator
Gondomania
Heavy Barrel
Midnight Resistance
Time Soldier