I'm sure you've already done the calculation, but for my own amusement here's my understanding and hopefully you can correct me where I'm wrong, and I'll assume myself 'cause I don't know some things about you:
Humans need to burn about 3,600 calories to lose a pound.
A sedentary male (ie, no active exercise program, spends majority of day sitting or lying) above 30 years old burns about 2,300 calories a day.
So if I eat nothing all week, I'll burn 2,300 just by existing, weekly burning 16,100, which is 4.47lb.
Now this doesn't actually work because your body does strange things when you have such a huge deficit, but so far as I know you can't lose 5lb a week without an extensive exercise program no matter what changes you make to your diet - except in the very early diet stages while your body is still running as though it has access to nearly limitless calories and burning more than 2,300 daily.
Every fast loss diet program only works for a few weeks.
Your 500 calorie diet, without much change in exercise, leads to about a 3.5lb week loss, which is only a little more than what you've found you're getting (2lb/week).
So while the early weight loss you experienced was nice, and you'd like to keep it up, I think you're much better off spending time on the diet you're going to have to maintain for the rest of your life. Your body will lose the weight slowly and you'll achieve a weight stasis that matches your intake and exercise level.
I'd advise you to go regardless of your stamina. Make it a priority, and a habit. Take full advantage of it starting now, because every day you're not using it is money down the drain, and because the little roadblock you've placed before you get there may lead to other excuses not to go down the road - moving the goalposts. Perhaps you've already moved them from "wait until the doctor says I can take a shower/get in water".
Don't let that happen. Even if it's just going, walking into the center, sitting for 30 minutes, then walking back out, make it important enough in your schedule that it becomes a habit - preferably a daily one. Turn on youtube or your favorite show, set the treadmill to a creeping slow walk, hold onto the bars and see if you can distract yourself enough to go beyond those 30 yards today.
You'll recover more quickly if you use the resources provided as soon as possible for as long as possible than if you wait.