MoonStarer

I have an Esprit, and mine arrived (from FLO) considerably cleaner, but not what I'd call pristine.

Some of the particles on your objective look suspiciously like brass from the focusser rack and pinion. Mine was quite poor in that regard and required a fair bit of cleaning up. Not something you should have to do on something this costly. I put up with mine as I enjoy the fiddling and fettling just as much as looking through a telescope!

I have one of those (got it from Starlight Instruments as I recall), but I don't think it would really be up to the job  of dismantling a mount like that. It's meant for undoing lens retaining rings, a much more delicate operation!

I've just done exactly this, belt modded and re-greased my EQ6 this week. 

I used this grease https://www.amazon.co.uk/gp/product/B007WR38TY/ref=ppx_yo_dt_b_asin_title_o09_s00?ie=UTF8&psc=1

The mount isn't  high performance engine, you could probably use butter and it would be fine.?

I saw this article on cleaning optics recently https://www.newport.com/n/how-to-clean-optics

This is from a fairly high-end optical supplier (laser optics), so hopefully their advice is ok.