Clean Further Or Let It Be?

I don't think you will be able to do much more cleaning without hurting the coin.

Unfortunately, that verdigris has eaten into the coin. If you remove it, you will find the detail has been obliterated where the verdigris was.

Curiously, I have a Roman bronze, where some silvering remains on the reverse, but the obverse looks much the same as the coin pictured here, with regard to verdigris damage.

The verdigris is removable, but to do the job properly would take hours, and would not be worth the effort, when all you are going to find is damage under the verdigris.