Dumbest thing about doing leg-day exercises in the morning? You still have to use your legs for the rest of the day. Didn't really think that one through very well.
I've decided to do strength training for just two days per week for now - Tuesdays and Thursdays - that way I can continue my normal Mon/Wed/Fri running schedule without wanting to die (too much).
So far, this has been a... humbling... experience. As with running, I'm sure there will be drastic improvement in the beginning, which sort of implies being absolutely pathetic at the start, but it's definitely frustrating when it's difficult to make it through your sets with an empty bar.
But! I'm having fun and learning new things, so that's something.