Update: I tried using the Tech21 Blonde pedal in rehearsal and it worked fine. I was unable to find what I considered to be an inspiring clean tone. I did not have time to go to a store that had various combo amps that might work for my needs (none nearby), so I ordered an Ampeg RB-110 since it seemed like it could meet my needs. I have been using it as a monitor (not running bass through my main monitor) and DI to go to the board. I have used this setup at rehearsals and 2 outdoor performances.
I am impressed by the tones I am getting and have found that with the volume at about 10:30 I can hear the bass well in rehearsals and performances. Also, this gives me plenty of signal going to the board (DI is post volume/tone) and is dead quiet. I am able to get a lot of great sounds by adjusting the tone knobs and the SGT, though I have mostly run the amp with the tone knobs at 12:00 and the SGT off. It sounds great to these ears at these settings. I am using a Mustang PJ, almost always on the neck pickup with tone open, with well broken-in Chromes, playing mostly but not exclusively with a pick.
At home, I run the volume between 9:00 and 10:00. I can sing at these volumes and still hear the bass clearly.
Thank you all, again, for your suggestions. I hope that my comments are helpful for others!