As long as your profile supports it, you should be fine to ask whenever you are ready for the PenFed and Chase cards.
If you have a green check mark offer with a specific APR in your Chase account that only asks for income and housing payment, that bypasses 5/24. I got 2 cards that way last year being LOL/24 and DW got another being over 5/24. My only suggestion would be to make sure that CSP and not CSR is right for you, as you'd need to wait a year to product change. CSR now populates as a green check mark offer; if you don't have it, perhaps you could talk to your banker to see if there is an offer for you that bypasses 5/24.
I don't think Chase pulls for savings accounts, but the CSP would certainly be at least a single (if not double) pull. That sounds like a solid 5/24-bypassing green check mark offer to me!
I'd plan on Chase doing another EX/TU double-pull. I had those bureaus pulled for me when I first applied for my card. When I requested a CLI, it was the same double-pull.
I asked a second-tier rep about the pulls, and she prefaced what she told me by saying "we're still trying to figure that out." She said that from the observations of the people she worked with, pulls seem to based on the customer's state. She added that generally, either Equifax or TransUnion is pulled with Experian as a "backup" — but that in some states, only Experian is pulled.
It's interesting that because the reps aren't told anything, they're working with data points just like we do here. The difference would be that they have a huge number of data points at their fingertips.
For CLIs or subsequent apps, I'd expect the same pull or pulls you got the first time around. If there's a change, it'd definitely be something that should be posted here. 
If you apply for anything, please let us know how the pulls shake out.
I'm (obviously) in MA, but for me Chase has always double-pulled EX and TU for new apps and single-pulled EX for CLI requests.
Chase also pulled TU + EX for me on the CSR.
