Hi, most of the issues you're talking about here are likely to be helped by increasing that first A time. LO is sleeping a short UT nap at the moment and if you increase that a tad, maybe 15min, you hopefully should see a later WU and/or a longer first nap.
From 4 months to 6 months, average A time increases from 2hr to 2:45/3hr, so 2:15/2:30 A time is pretty reasonable at this age.
In the meantime, if you're aiming for a 7:30 BT, don't wake her from a catnap at 5:30 after a day of short naps, wake her more like 6pm which would give her a better chance of getting to 7:30. It depends on your wishes a bit here - you could do one longer day and hope she pushes her WU later the next morning and just start your routine from there or you can gradually do it with the slightly longer A time first thing in the morning.
Where is she having that first nap - she can clearly sleep through that transition and have a long nap, so that's not what causing the short AM nap... Can you write out what your day looks like family-wise, so what times are drop-off and pick-up, how long does it take, does she sleep during the process, if relevant, what time does OH leave/get home in the evening, is this consistent?
IME, in this 4-6 month period, most LOs become able to have a day of 12-13hr with an 11-12hr night and the day naturally has to elongate before shrinking when the catnap goes around 6 months/3hr A times.
