Welcome to the forum, Weston! I skimmed the Yamaha manual, and I don't think that you're missing anything. It's oddly typical of stereo receivers with sub outputs to not have any bass management.
Others should chime in if they disagree, but I don't think that you'll hurt the NHTs by sending them a full range signal - you just won't be able to hear low frequencies because they won't play them. I have NHT 1.5s that are bookshelf speakers, and I've played them full range without any problems at all.
The issue is getting the NHTs and the sub integrated together sonically. That's the great thing about bass management, as you know. If you use the line level input to the sub, you can adjust the crossover on the sub to try and get a fairly flat overlap between the low end of the NHTs and the high end of the sub. You can also, as you said, use the speaker-level inputs and outputs on the sub to get a nice, clean blending between the NHTs and the HSU.
I don't have experience adding a high-pass filter to speaker-level signals, so I'll leave that to others here that know more.