Yes I've fought these exact issues for decades. Two revelations for me, both occurring about 12 years ago. I simultaneously switched to flats, after playing rounds since Christ was a corporal, and I went low powered tube amps after playing solid state since day 1. First, unlike rounds, the flats don't disappear as soon as cymbals or guitars start playing. The initial thump of the flat wound attack and the relatively low sustain allows for a dominant bass without it being overpowering. Second, to my ear the harmonics added by the power tubes before they reach breakup adds a "halo" to the bass that makes it distinct in the mix but again without being overpowering. Pushing the tube amp to this point, if you hear the bass soloed it is obviously distorted, but in ensemble it has a pure, round quality. The advantage of the low powered tube amps is I can push the power tubes to this point at a very reasonable volume. I am now playing medium and large stages with my 50 and 100 watt tube rigs and flats, and my bass is more distinct and present than when I was blowing 500+ solid state watts with rounds. Also, in my experience this effect isn't achieved with tube overdrive from a pedal or preamp and a solid state amp, at least not nearly to the same degree. The power tube distortion is a much different animal than preamp tube distortion. Also just to be clear, I am not going for a distorted sound. As I said, when you're hitting the sweet spot, the bass in ensemble does not sound distorted. But once you learn to play the amp, you can get it to the point that you can push it into breakup just by digging in a little harder, then back off and there's your round tone (at least your ears tells you it's round). Also just to say, I don't use any pedals. Another side benefit of pushing the power tubes like this is they enter into a really nice (if it's a well designed tube amp) self-compression that doesn't just beat pedals, it rivals studio compressors.
So the upshot is, I'm now 71 years old, and I'm happily schlepping tube bass amps around and getting the best sound I've ever had.