Huh. I always orient the edges before I start to go try to solve them. Maybe that wasn't a good example. Is there a possibility I could end up in that same situation with the edges oriented correctly?
No. If your last six edges are all well oriented, then situations like the example above never could happen. If your UL/UR edges are on the DF/DB places, then the L and R stickers (in the previous example: white and yellow, in the new exaple: red and orange) always on front and back, therefore, the insertion in step 4b) is easy. That is because your all 6 edges are well oriented - including the UL and UR edges! If it's not the case (again, like the example above), that means your orientation is wrong, therefore, you didn't finish step 4a) yet.
From this tutorial:
General Rules for UL and UR Permutation.
1) To preserve the EO, you can do M2 moves and U moves to permute stuff into place
2) It's okay to just use an M' or M move as long as you follow up with a U2 and another M' or M
I think I may be doing that part wrong. Would M2 U2 M2, or M2 U2 M' follow those rules?
That means if your edges are all well oriented (hence, finished step 4a), moves loke M2, U and their combinations don't mess up the orientation - each 6 edges remain well oriented. Only M and M' moves changes edge-orientation,
except it follows U2 and another M or M'. In long, the following moves
do not change orientation:
M U2 M
M U2 M'
M' U2 M
M' U2 M'
Therefore, after finished step 4a), you can use all of these (and many similar more) to solve Step 4b), and you don't need to worry about missing up the edge orientation in Step 4a).
Your example M2 U2 M2 is good here, but M2 U2 M' does not - unless you continue it with U2 M or U2 M' (if not, it messes up orientation, if it was good, and bring you back to an unsolved Step 4a).
The way I get into that bad situation is usually when the edges I need to be across from each other, are right next to each other like this:
U2 B2 L2 D' F2 L2 B2 U' R2 U2
After fiddling with it a little, I think I figured it out, but I still don't completely understand.
In this example, I assume that your blocks are orange-yellow and red-yellow, and your UL/UR edges will be white-orange and white-red. Here, every edges are oriented, Step 4a) is finished.
Step 4b)
M2 U M' U2 M // Place UL/UR edges (here: white-orange and white-red) to DF/DB places for easy insertion
M2 U // Place UL/UR edges to their final place
Note that here the orientation does not change, every edges remained well oriented, since a singe M or M' was never used,
except where U2 M or U2 M' followed. This is exactly what I said above. We don't want to mess up orientation done is Step 4a (which is skipped here, since we already had well oriented edges).
Step 4c)
M' U2 M' U2 M2 // Solve the remaining permutation on the M slice. Note that again the orientation does not chage.
Solution on alg.garron.us
