Hey Bret, welcome and nice to hear from you, albeit I wish it were better circumstances. I've not heard of this behaviour/problem before. I tend to agree there seems an issue with the gate in/out, but more complicated, if that's all it was/is, then the threshold setting should work. Can you select gate mode options (fader/gate), I use MP-2 and am assuming the gate is similar in the Classic where Gate mode is a hard gate and Fader fades the sound. From what you describe, the gate is turned on and the threshold is set quite high and you can't change it. A not so great (slight) work around is crank up all your drive settings and turn the master down, thus providing max signal to keep the gate open, although it's not a fix. Also if you crank up the compressor, that will also increase the signal and help keep the gate open (but stuff your playing dynamics).
IIRC a new(ish) member Gregg was looking into the clamping circuit and its components for the MP-2 (again which I assume is similar if not the same), and maybe he can chime in with some ideas? You can find Schematics here
https://adadepot.com/index.php?topic=148.75. I suspect the gate is either part of the compressor or maybe the chorus schematics? I had a look and it's above my pay grade LoL. Though it makes sense that the gate is before the chorus, just after the gain stage (so you don't chorus noise).