Hi
It looks like your LO is waking earlier because her first nap is coming at 7.30 on the school run so in effect she is giving herself the A time she needs prior to that nap (which makes sense really).
One option would be to just let her get up at 5.30 as the routine is kind of working for you in that sense - and get yourself to bed an hour earlier too so you don't miss your own night sleep.
Another option would be to shift the whole day on aiming to avoid the car run nap and her not being tired until you get home. For instance waking at 7am and not being tired until 9.15am then being able to do a good nap at home. Of course if you shift the day on it impacts on the timing of the afternoon nap too and that could be a good thing or not for you.
There could be a chance of:
WU 7
A 2hr 15
S 9.15 - 10.45 (1hr 30)
A 2hr 15
S 1pm - 3pm (2hr or waking at 2.45 for school run)
A 2hr
CN 5 - 5.45
BT 7pm ish or whatever suits based on having had the CN, it could be a bit later than 7pm but you probably don't want it earlier if you aim for a 7am WU next morning, if anything it could be later than 7pm, maybe 7.45pm or 8pm to allow for 11hr night sleep which is what she's currently doing.
She's probably a bit young to drop the CN and go for EBT, I would be concerned that it could cause some OT leading to EW or that if it did not cause OT the EBT would not help to shift the WU time the following day. Of course you know her best though so take all your knowledge and experience into account when considering my ideas
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Not a simple solution but perhaps some options to think about.