I'd think Dudley would go first since Popeye is more popular and already has a cohesive mini-land.
If you bulldoze Dudley, Comic Strip Lane, the carnival games and the TL theater area, there's probably room for 2-3 decent-sized attractions and 1-2 smaller additions.
I'd guess the phases would be:
Phase 1 - SLoP E-ticket and Sing mini-show in TL theater area
Phase 2 - revamp of Comic Strip Lane
Phase 3 - Dudley bulldozed for family dark ride and family coaster (or one D/E and 1-2 smaller attractions)
Phase 4 - whatever happens for Popeye (update or retheme)
Popeye is just too much of a crowd pleaser to close down for 9+ months IMO and it's the one water ride at IOA that doesn't need any drastic changes.
JPRA needs some major overhauling and Dudley takes up valuable real estate (could make a dark ride or family coaster work in its plot) in a land without relevance while Popeye's space is pretty much limited to rapids ride due to its proximity to the IOA lagoon.
Once all of TL is updated or fixed, I could see a Popeye revamp/retheme, but currently, it's fine as it is.