Hi there:) I have a 9 month old too. Let's see if I can help you out. Firstly, I completely agree that he is not getting much sleep at all during the day. Due to these early wakings, your day is also very long- nearly 14 hours. It is best to aim for a 12-12.5 hour day, and on days with such little sleep and EWs, i would go for an early bedtime. So basically, if he wakes at 5.30, i would get him into bed by 6 latest.
What I think might also help is distributing that sleep a little differently. Around this age, babies start the 2-1 transition, which in itself is a long process, and it is not possible to fit two long naps in the day, without extending it too much. So a better option is to go for a long nap + CN. You can either do short morning, long pm nap or vice versa. Eventually you can drop the CN and go for one nap with an EBT.
If it will help, our routine is
7- WU
11- 1--nap 1. ( anywhere between 1.40 to 2 hours)
30 min CN after 4.10 A
Bed 1.5 hrs later ( she needs a short A to bed)
Bedtime changes depending on CN but usually between 6 & 7