That's exactly where Logan takes place - 2029. Six years after DOFP's epilogue. Given Logan's dialogue with Caliban in the beginning, Xavier probably had his breakdown about a year prior in 2028, forcing Logan to move him away to a secluded location.
FC (1963) -> DOFP (1973) -> Apocalypse (1983) -> DP (present day) -> DOFP (2023) -> LOGAN (2029).
DP's an interesting case because I was reading through the shooting script and Wade's overall journey takes over the course of 5 years, and the film doesn't say it's set in 2016. So there's probably some flexibility as to where DP is set, esp with their own time travel shenanigans about to begin with Cable's introduction.
Legion probably takes place near our present day as well, depending on how old Ptonomy is because his memories are basically the clue as to when Legion itself is set. (But I wouldn't worry about Legion's time period, since it deliberately has anachronistic elements).
Gifted is present day, in the post-DOFP timeline, with a younger Blink.