I've definitely had *held* flights that had some overlap (or even those that didn't overlap, but were mutually impossible, i.e. IAD-SFO leaving at 3 PM and IAD-SFO leaving at 6 PM the same day) and found one summarily deleted. I can't say for sure if they would do the same to overlapping ticketed flights, but I do think UA definitely tries to discourage this type of thing.

I do suspect that booking one or both without your MP# might make them less likely to get flagged. Also if you could make a minor variation to your name (e.g. JOHN A SMITH on one, MR JOHN ALEXANDER SMITH on the second) that might help too...as long as it isn't such a variation that it would be an issue with your passport/travel docs (since you said these are mixed LH/UA I assume these are international trips).