I have a Scottish friend who swears the best way to make himself understood abroad is to put on an Italian accent. Make of that what you will.

Personally I mostly just stick with avoiding idioms and speaking a bit slower but then my native accent is pretty close to British Received Pronunciation.

When I was living in Scotland for 10 years I went the opposite direction - I felt I'd be less judged as a posh English shite if I moved further from RP (in my case that just meant upping the natural estuary English parts of my speech, not trying to go Scottish or anything stupid like that).

Some native English speakers though, especially the ones I know in Britain and have known for a while, I think of as so fluent I don't even think to change my speech patterns.