I know what you mean about those pesky triangles! They're difficult enough when they're the only shape you're using. When it's time to add one to a corner - Oy!!! I have yet to make a star quilt on which every point matches.
Paper Piecing is one way to go. IF you manage to stay exactly on the lines and IF you keep every seem allowance the same as all the others, it'll come out either perfectly or close enough that disjointed points only show themselves on close inspection.
If I'm adding triangles to a corner (e.g. snowball or flying geese blocks) I start with patches cut slightly larger than they "need" to be. I don't stitch exactly on the diagonal line. I stitch at least a 16th of an inch inside (toward the corner of the block underneath). Then I fold it back to match the block and press to make it line up with the square or rectangle. If you're going to trim away the extra layers, don't do it until it's time to put the block together. Make sure everything lines up, re-pressing here and there if necessary. Once it all lines up, it's less dangerous to trim.
You can also press the square into a triangle, lay it on top of the patch underneath and hand or machine baste into place. If you don't trim away the extra layers underneath, you're left with what can be some interesting added dimension once it all goes together and remove the basting.
Or, using the same basic method, machine topstitch to both keep the triangle in place and embellish to the block and top.
If I'm feeling especially OCD about a project, I even pin or baste before machine stitching the patches together for the block; then repeat when putting the blocks together for rows; and baste the rows, etc.
Keep checking this thread. I'll bet you get several suggestions from quilters who get more success than I do with triangles.
I'm sure there are many other methods that work as well or better and which - with practice - make the whole process faster, but these work for me. I just have to live without the instant gratification of a top that goes together in a day or two.
I can quilt quickly or precisely. Haven't yet mastered the art of doing both at the same time. (And I've been sewing since I was 5 years old. It's easier to match plaids in a suit than it is to get those durned points to come together! LOL) I stand in awe of those who can do it without a slide rule and super glue.