Here are my replays to the two levels. Not sure if One-Way Rock is a backroute, but it looks like it follows most of your guidelines on how the solution should not be a backroute.
TL;DR for the upcoming description of your solution for One Way Rock:
It is not a backroute. I got carried away in my description of why it's an acceptable solution (complete with screenshots!), so if you want to read it, there's a nice long explanation about it.
Close enough on One Way Rock. My intended solution digs slightly further down the one-way-down obstacle and uses the miner from the left side of it, but I typically don't mind minor variations on my intended solutions, and your solution definitely counts as a minor variation. It doesn't look like it would be too difficult to modify the level to enforce what I'd intended over your solution if I
really wanted to but I don't think there's any reason to do so, since they're so similar.
Screenshots:
My solution is on the left, yours is on the right. They are similar enough that I don't consider your solution to be a backroute.
You might notice that I used an extra basher. When I choose my skillsets, I prefer to make things generous enough to avoid precise assignments when doing so won't create backroutes, so that basher is only there so you don't have to worry about the miner placement as much.
Your solution to the other level is pretty much identical to mine.
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I don't believe I mentioned this in the post where I submitted the levels, but I'm not horribly attached the names of them. If anyone has a better idea for the names, just run it by me. If I'm okay with the alternate suggestion, it's perfectly fine with me to rename them.
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Should I avoid specifying music tracks? I didn't really think about it when I originally submitted the levels, but since NeoLemmix has the ability to do so, I usually specify a track that I feel goes well with the level rather than using randomness or a set order.
For reference, One-Way Rock is set to orig_17 (Coming Around the Mountain). The other level doesn't specify a track, probably because I made minimal changes to it, and therefore it required minimal testing.