I bought a "Stinger" Perfect Delux Reverb copy ...
Now that I have to get some volume out of it, I find it distorting with the lower notes above a certain level. ...
What is that "certain level"? A Deluxe Reverb only gets so loud before it distorts (and it will get a "fuzzy clean" before it's obviously distorted). Are you sure you don't just have it turned up beyond its clean output power?
For example, by the time a Deluxe Reverb is making enough volume output to hang with a drummer in a small-club setting, it will distort. Which is why a lot of players in the Nashville bars liked using the Deluxe Reverb: You could use a single-coil guitar, turn it up to have gig volume and get good distortion without killing folks in the front row.
The above assumes a band
which plays with dynamics, meaning the rhythm guitar player knows how to back off his loudness when the lead player needs his lines out front. I can't overstate the importance of a group of players who know how to not step on each other in a performance.
By comparison, my Princeton Reverb used in a band setting cannot be heard with a drummer/band even all the way up loud enough to be a soloing amp... at least not without mic'ing the amp into the PA. Distorted rhythm guitar, no problem, but not loud enough to punch through the band for a solo.
At least, that was my experience taking a number of amps to blues jams: Princeton couldn't cut it, Super Reverb on 6-7 was perfect as long as I work my guitar's volume or laid back when not playing lead, Tonemaster amp bigger than really called for but could be clean or dirty at any usable volume (but that was 100w and a beast to transport for a non-paid fun gig).