I can totally relate to this situation. I work as a PA and twice a week I first assist in spine cases. Typically these days are 12-14 hours, similar to your shifts. They can be exhausting. Scott mentioned that they certainly don’t make you fitter, but can absolutely add to your fatigue. There are a handful of things that I do to help reduce the impact of these days. Here are a couple that I have found to be pretty effective for in the OR: compression socks and/or compression tights on really long days, if your hospital allows invest in your own lightweight lead (the one I wear is 11 pounds and cost around $400), if possible in between cases or on breaks I spend 5-10 minutes laying on the floor with my feet on the wall above me, get off your feet whenever possible, even if it is for a minute or two at a time it adds up.
As far as training on those big work days, I have found it pretty challenging to get in any hard efforts on those days. I do find that I can get in some easy running or cycling in the morning before work, most commonly this has been commuting to the hospital from home on foot or via bike. For me that is about 7 miles each way and the easy effort in the morning doesn’t crush me during work. An easy spin on the bike for 30 minutes or so after those long days seems to be pretty beneficial for harder training the next day. Normatech boots have been a huge benefit for me. I use them in between cases when there is enough time, and have found that a 15 minute session after a long day in the OR can freshen the legs up enough to feel decent enough to get in a good workout.
The hardest part of the situation we are in is finding the right balance of work and training. Scott has done a wonderful job of teaching me that it is ok to skip a workout if you are crushed after work. You know it is going to be 3 days a week, plan your hard sessions around those days, and figure out what you can or can’t do on work days without impacting the quality sessions on non-work days. Also, make sure you prioritize time with your family!