I'm posting this with the usual warning that diagnosis cannot be made from a distance and health problems should be addressed by your own personal health care professionals, not a random person on the interwebs with who knows what qualifications. Having said that...
If the hot foot was coming from something related to foot position itself, I would expect it to get better with spinning, not worse and I would expect it to be helped by the orthotics. So it seems likely that your foot pain is not coming from your foot but more likely from someplace else in the kinetic chain.
The next most likely culprit is your back/hip and I think this is likely the case for you. Spinning requires you to put more weigh on your saddle and less weight on your feet as you are concentrating more on pulling back and up during your pedal stroke. Chances are that something is happening here that is causing you to round out your lower back and put pressure on the nerves that come out of your spine and ultimately end up in your feet. I can think of two possiblilities off the top of my head.
1) You have a muscle imbalance around your hip that results in relative weakness at the top of the pedal stroke and to compensate you are rolling your pelvis under at the top of the pedal stroke which also flattens out your back. The easiest way to test this theory would be to try some single leg drills on a trainer where you are completely clipped out on one side. If you have the weakness I describe, you'll have a dead zone (difficulty moving through that range and/or clunking) at the top of the pedal stroke that may not be present right away but will be present as you fatigue. If you can't do at least 1 min without this happening, it could be the culprit.
2) Your saddle is uncomfortable in some way, most likely too much pressure around the pubic area, such that it makes you want to roll your pelvis under to relieve the pressure. When you mash, you take more weight in your feet and less on your pelvic triangle so it might not bother you then. You can check this out by trying to play with your pelvic tilt on the saddle as you ride.
There are lots of different reasons for developing hot foot. But these are a couple to consider, especially if you have a history of low back issues.
Living life like there's no tomorrow.
http://gorgebikefitter.com/
2007 Look Dura Ace
2010 Custom Tonic cross with discs, SRAM
2012 Moots YBB 2 x 10 Shimano XTR
2014 Soma B-Side SS