What about about async or defer loading script?

I’ve tried experimenting with these and I haven’t found a good solution for async to work with the counter script.

It would be right way, I think, to have async loading of the script. Hope you manage to find a good solution.

You could potentially try using: https://en-gb.www.ads-software.com/plugins/async-javascript/ which is a plugin to async javascripts in WordPress and test if this tracks.