I'm sure I'm not the first person to have come up with this and that at some point over the last few years, this idea has been presented in the forums, but I just wanted to share my experience with everyone and spread the idea!
I played a solo game today with 4 investigators and the Innsmouth board. I split the Mythos deck into two piles, one made up of the base Arkham Mythos cards and the other made up of the Innsmouth Mythos cards. Being that there are 9 neighborhoods in Arkham and 3 neighborhoods in Innsmouth, ideally it's a 3/4 chance that a gate would pop up in Arkham and a 1/4 chance that a gate would pop up in Innsmouth.
Every Mythos Phase, I would roll a D8. On a 1-2, I picked the top card of the Mythos deck from the Innsmouth pile. On a 3-8, I drew from the base game pile. At least for this one game, it worked wonderfully.
This technique would work for any number of boards you want to play with. For example:
Arkham + One Board = Use a D8
1-2 Extra Board Mythos Card
3-8 Arkham Mythos Card
Arkham + Two Boards = Use a D10
1-2 First Extra Board Mythos Card
3-4 Second Extra Board Mythos Card
5-10 Arkham Mythos Card
Arkham + Three Boards = Use a D12
1-2 First Extra Board Mythos Card
3-4 Second Extra Board Mythos Card
5-6 Third Extra Board Mythos Card
7-12 Arkham Mythos Card
Typically when I play, I only add expansion cards to the Mythos deck when I'm actually using main mechanics from said expansion (an extra board, Lurker Herald, etc.). I have played many games with these combined decks where I would draw Mythos cards from the base game cards only, rarely ever getting gates to pop up in Dunwich or Innsmouth. It's so frustrating to set-up an expansion board and get excited to experience a true add-on to the base game, only to never have to travel to another board, except maybe for clues.
Playing this game with this technique really brought the extra board to life and made it feel like an integral part to the game. I'm going to test this method out with future games and get the opinions of the other people in my Arkham Game Group.
Hopefully someone likes this idea and can try it out in their game(s)! I'd love to hear how this method plays out for others and if it makes their games better!