Thanks for the comments metrologist.
Today I gave the scope a good cleaning. Cleaning took a good 4 hours. But it looks super clean now. And the screen is just about perfect (the picture below has some reflections of an office chair).
First, I opened up the case to blow out the dust with canned air and look for any obvious issues. There was very little dust and the boards looked like new. Iwatsu did a very tidy job engineering and assembling this. Two outside case screws were missing so will need to find some spares.
As you can see in the photos, the multimeter / counter just looks like a separate board option which did not fit inside the case, does not seem packaged to sell as a stand-alone unit (and I found nothing stand-alone similar to this box). I assume the counter is independent of the scope (scope's 1k calibration shows about 1.005 on the counter). There is a somewhat dodgy copper ground strip running from the counter's external input which would be easy to rip off when putting the metal case back on the scope.
Aside from blowing out the dust, I used barely moist rags (with very little mild dish detergent) to clean the case and front panel. Worked suprisingly well. I removed the 3 big clear dials for deep cleaning. Then I removed the screen cover and used compressed air followed by moist computer monitor wipes so not to damage coatings. The multimeter/counter face was more dirty/oily so I used some isporopoly alcohol with cotton swabs on that section (and input jacks /grounds). Iwatsu recommends certain cleaners in the manual linked above.
Finally, cleaned the leads and power cord with a bit of detergent on a barely damp rag. Those are still just slightly dirty. What is a good product to clean the probes without destroying the soft rubber?