[jackblemming]

>I have some positional power, so I can experiment a little with not-so-much resistance.

I've found power from being competent to be more effective.

>While we were in-office we could do simple over the shoulder code reviews and exchange valuable feedback fast without any official process.

What is this trying to solve that regular code review doesn't? Why does it need to be over the shoulder?

>what changes can we start making in our team to introduce code review practices to make the code quality better and avoid the common mistakes?

Require code review for any non-trivial change?