Success! Teledude, I really appreciate your guidance on the process.
I applied DeOxit5 to the 4 switches beneath the display, as well as to the Levels and Line switches. After 30 minutes or so, I checked the result. The problematic switch needed a couple of pushes to bring up the brackets. So I zapped it again. After a while I checked again. Noticeable improvement. Sometimes one push was enough.
After the 2nd DeOxit5 application, I called Studio Electronics because I wanted some feedback. Tess, who has hands-on experience with this process, said, based on the progress after two applications, a new switch was not necessary. She said if the switch was not fully operational I should continue applying contact cleaner as many as 10 times.
The next day (today), a single push consistently brings up the brackets!
Before, during, and after the above, I was wrestling with purchasing an H9000 (not as a replacement). Success with servicing the H3000 might have contributed to deciding to go for it. Feeling I’ll have 2 discrete bases well-covered.