So for endmyopia you would generally use two pairs of glasses, one for distance that is very slightly undercorrected compared to your full prescription for distance; and one pair of glasses for close-up.
In your case it sounds like you need a pair of distance glasses, and you might investigate whether or not you could remove a small amount of the astigmatism correction for close up and still see the screens well. Many people find they don’t need as much astigmatism correction for close-up as they’ve been prescribed.
So in your case, rather than going without glasses entirely right now outside (which if I understand is giving you headaches) you need a pair that almost entirely, but not quite, corrects your distance vision. Perhaps right now without glasses you see 20/60. Let’s say you get a pair that corrects you to 20/25 vision instead of 20/20 vision. Then when you’re wearing those (whenever you’re outside doing whatever you do outside) you practice focusing on distant objects through them. After a few months of wearing those and focussing through them you should be able to see 20/20 or better through those glasses, at which point it’s time to remove some additional correction.
So instead of being outside walking around and getting headaches from too much under-correction, you should be outside and walking around practicing focusing on distant objects. Usually after about 3 months you can reduce the correction a little bit more.
The time commitment is really up-front just to figure out what it is you’re trying to do (the stage you’re in now). It’s not like you need to set aside part of your day to “do something” you’re not already doing.
In your case you’d want to figure out what your “full prescription” for distance is, and then start with a little bit less than that to get some focus challenge.
Read up a little here on “blur adaptation” and how to combat that. You’re probably blur adapted from not wearing distance correction.