I keep the randomizer deck in two stacks. When I pick a kingdom, I take the top card of each stack, pick the card that I prefer for the developing kingdom, and put the other card at the bottom of its respective stack. It’s a good middle ground between total randomness and having to consciously choose a kingdom every time
I’ve only gone with truly random kingdoms but I like this random+choice suggestion, I might have to give it a try.
Edit: I wonder if you could incorporate some sort of blind voting mechanism so that all players could collectively vote on each pairing.