How to replace porch joists?
it depends how far those holes go. if you can over-feed one end of the joist, you can then align the other end with with the other hole and 
back it in. 

ledgers, as you suggest are a legitimate solution too, also brackets, but on brick ledgers are easier. 

ledgers both sides is probably the easiest to get right. you're then not relying on any unseen features of the building construction, and avoiding any potential unpleasant surprises.