Typically I play with my left hand playing chords/notes and my right hand picking. I decided to switch it around today after curiosity and noticed that my right hand is just...better. I know that being right handed helps a lot but I am stronger in my right hand and can span a fret more than my left.

Should I keep plugging away at it with my left hand and know that someday it will gradually get stronger and more flexible? Are there any exercises, besides playing scales, that I could do away from home?

I'm just a little bummed out; I don't fancy the idea of buying a left handed guitar or reverse stringing my electric guitar from what is the standard.

Anyways, thanks for listening and thanks again for any help!
It depends, everyone is good at fretting with their right hand, (if their righties) but are you efficient at picking with your left. If you then i think you should try out at lefty guitar or something and see how it feels, how long have you been playing righty for though?
theres sorta a reason why you should work with your off-hand fretting and your dominant hand picking. Your body uses its 6th sense to monitor where the position of your non-dominant hand is, and it uses sight to keep track of your dominant hand. What this means is that your going to run into huge co-ordination issues with having to look at both your right hand when fretting, and building accuracy picking with your left. Just go ahead and keep using your non-dominant hand to fret.