Personally, I use LastPass across browsers in multiple desktop accounts and my mobile browser, with no issue. You create a LastPass account, presumably with a very secure password, that you can log into elsewhere.

As for the password strategy, I imagine you could be vulnerable if any two important accounts - say, email and bank - both used the same password. Are you confident this is not the case?

I assume certain emails associate with certain types of accounts, which could flaw your strategy. If you're able to remember ~15 different passwords with random emails, congrats on your stellar memory!