Most of the time it's as simple as switching out your "near" lens to your regular distance power. You will of course lose some of the clarity at your near distance, so you might not be able to see your maps, instruments etc. but it will most likely improve your distance vision, thus allowing you to just buy a pair of good quality sunglasses without throwing in the added expense of prescription Rx spectacle lenses. When the Doc writes your Monovision RX, he writes it for one eye to be focused at the "near" and one eye at the "distance" as you mentioned. You would just need to go back and inquire on getting a new set of lenses for the eye you want to convert bk to distance.
I hope I didn't totally confuse you. LOL