I'm in exactly the same boat, and ended up on Go Read, but recently I was looking for a solution which had better mobile support and came back to Feedly.

Created an account first and checked whether you can export your OPML, and indeed you can in the feed settings: https://i.imgur.com/ttPNrd1.png

The mobile app is great too, it has become my main RSS reading platform.

Same. I used google reader heavily when it was around. Now I don't bother using any 3rd party service and I just host my own RSS server (tt-rss). Not going to start using a service and get used to it, only for it to shut down.

I think you can back up OPML to Dropbox, which should provide kind of export facility, since OPML is a generic format.

Feedly does OPML import/export now. It worked for me the other day.

I'm just a (non-paying) customer.

https://blog.feedly.com/opml/

Ah, didn't know that. Even better, thanks for the pointer!

I didn't even use a service like Google Reader, but when it died, I got caught up in the flood of alternatives, and am now a very happy Feedly user.

Didn't even know what I was missing!