First off what most of the homebuilders seem to do is only use the mitre cuts on outside corners. You normally find they use a copping joint on the inside corner of the rooms. A coping joint is much easier to fit the first piece of trim is straight cut and put up on the wall. Then the second piece is backcut using the molding profile. With a little practice on scrap pieces this can be learned fairly quickly. A coping saw is a a low cost hand tool. The outside corner will need to be mitered. As we don't live in a perfect world the angles as you found are not perfect. The quickest way I have found to set it up by using scrap wood. This doesn't need to be molding it can be 1x2 or something. Set your miter close to what you think you need. Set the scraps in place on the corner you need them to fit. Then make very small adjustment on the angle of the saw. recut on scrap again then fit again. once you find the perfect angle with the scraps you can cut your trim boards.
I found that the coping joint method was the only way foreward.
This was because my house is old and the walls are not at right angles. Your mitre saw relies on a nintey degree wall to work off.
For a duffer like me plenty of sealent and sawdust filled the gaps (no use unless you are painting though)