How should I hang joists that are supposed to be doubled, but that will sit over the joining of two boards?
If I understand your question correctly, the problem is that the green highlighted double joist is going to land on the joint between your two boards making up the 22' ledger attached to the house.
I see a couple of options:

So long as the fasteners (ledger to wall) aren't in the way of the joist hangers, have the ledger joint right there and use a standard double joist hanger.

Make your ledger out of a 12' and a 10' board, thus moving the joint between ledger pieces away from the doubled joist and eliminating the problem all together.  This could move the joint to behind another joist hanger, which could present the same issue, but in a different location, so...

Make your ledger out of two 12' boards, each cut to an appropriate length so that the joint falls conveniently between joists. This allows you to securely fasten at the edge of each ledger board and to use your joist hangers without fear/concern about running into the fasteners at the edge anywhere along the line.


You'll probably find that even two 12' boards are going to be cheaper than a 20' and a 8' anyway. 20 footers are pricey, especially since lumber prices have spiked over the last 6-9 months. I don't recall my local big-box lumber yard selling 18' lengths - I believe the standards are 8', 10', 12', 16' and 20'. Since the ledger will be firmly attached to the house, it can be made up of shorter pieces without worry.
If your calculations show that the joint between a 10' and 12' board will not fall behind a joist position, option #2 would be easier and less expensive, so option #2 would be preferable. Don't forget that you can put either board at either end, so you've got 2 possible locations for the joint.
If you can't make option #2 work out, go with option #3.
Honestly, if the pricing and spacing works to your advantage, you could use three 8' boards as your ledger.