Inside latch
Hello,
We have recommended the 40-150 as a possible replacement for old-style storm door latches like yours in the past. The shape shouldn't be an issue but I can't be positive if it would reach your keeper since you don't seem to have much space to adjust the position on the door frame.
The only other option we could provide would be to replace the entire handle set with something like the 40-177, which comes with keepers for the deadbolt and latch. Review both options to see what you think. If you decide to give one of them a try and run into any issues, our return policy can be found here. Thanks for posting.