You seem to be painting a grim picture here, Chasing, but perhaps the policies in your airline have led to dirtier-than-average cockpits?

(you don't work for BA, do you?)
I have to agree, however, there seems to be a general trend toward dirtier cockpits. There are probably quite a few reasons for this.... Less manpower allocated to cleaning, faster turnarounds, budget airlines lowering the standards... or it may even be overzealous safety officials not allowing cleaners into the cockpit even to clean the floors. The jack-of-all-trades engineering policy is not helping things either. As an Avionics Engineer, there was a time when my jacket was rarely dirty, but now I am expected to change engine oil, inspect greasy undercarriage, etc. (However, my jacket may not be as bad as it looks. The grease stains are probably a few years old...the ones which have defied dry cleaning. The probability of the stains being transferred to the furniture is probably quite low

). BTW, if our cleaners are working on our cockpits and I am sitting in the front seats, I will assist by cleaning under the chair and in the footwells with their vacuum cleaners
Re dirty seatbelts. Unfortunately, this is a specialized area. If you put it in the tech log, it may take a while for the problem to be rectified. We can't use any old cleaning product and the stains are probably not of the easily removable kind. Lots of effort will have to be expended to replace the belts (It's not a job you want to attempt on a quick turnaround).
Another thought.... Maybe management(s) are deciding that now that the flying public is not allowed on the flight deck (as jumpseaters), there is not the necessity to keep up such high standards?
Unfortunately, once the rot has set in... things will probably get worse. It's like walls being graffiti-ed (sp?). The faster you clean up the wall, the less likely it is to be re-graffiti-ed.... and if one is presented with a dirty cockpit, one is probably less likely to make an effort to keep it clean.
Perhaps we (engineers) did take offence where none was intended, but, if you're offering an apology, I won't say no
Anyway, I wish you luck with your quest, but judging by the forum response, I think you'll have to take your ideas to management (presenting yourself in large numbers) and let their policies filter downwards.... rather than risking the ire of individual engineers

Perhaps health/safety are the key issues here... rather than "appearance"?
Best regards.
NSEU.