It's happened to me on multiple occasions where my lug nuts will get stuck trying to take off a wheel. Usually it requires taking it to the shop to replace the affected wheel stud.

I understand this is usually caused by shops using a impact wrench to thread the lug nuts. However, my question is not about the cause. I was wondering if I were on the side of the road with a flat tire and I experience this while trying to change the tire, what is the best course of action?

In my experience continuing to force the lug nut off with a tire iron either results in flattening the threads on the stud (very noisy), or just snapping the stud in half. On a car that normally has five lug nuts, how many can I risk damaging before I should just stop and call a tow truck? Mind you this is just to get me home, and to a shop the next day - I would not plan on driving with lost lug nuts for an extended period of time.

Or would I be better off (both monetarily and safety wise) just calling a tow truck as soon as any lug nuts appear stuck?

Thanks for any tips and info on this problem.

Not sure if the cause of the thread damage is correct, but to address your question, I'd call the service before attempting taking off the wheel. This way it's their responsibility if it gets stripped and I am sure they'd have a trick or two on how to avoid that. If you get the AAA with a good plan it should cover at least three service calls per calendar year.
As far as how many lugniuts is safe to "loose" i'd say on the 5 lugnuts configuration probably 2, but it more depends on how far you have to drive home and at what speeds. I am almost positive that you could get home from couple of blocks away even on two lugs slowly, but would not be able to get on the freeway (and stay there) with only two out of five...
I used to live in Wisconsin for 11 years and I recall that after I started using the anti-seize grease (i am still using it on all my cars even though it's absolutely unnecessary in SO Cal) all my stripped studs/lugnuts problems disappeared. Try that & see if it works for you.