Oh OP, I really feel for you. It’s so hard. It sounds like you have a very overtired baby, with poor naps resulting in poor nighttime sleep, resulting in poor naps etc etc - it’s an awful cycle.
I’d suggest the first thing to do is to try and work on daytime naps. If your LO is only doing 30 minute naps, then he’ll need at least 4 during the day, possibly 5, depending on wake up and bedtimes. With that kind of nap length, he’ll only cope with a maximum of 90 minutes awake before needing a nap, so your 9am nap is probably already too late, hence why he’s already overtired and grizzling. How do you get him to sleep in the day? Is there anyway he can nap before your nursery drop-off, or on route?
I agree with the PP that the 2-3-4 method is great (my 8-month old switched to this at around 6 months), but they need to be napping for longer than 30 minutes to manage that many hours awake, so for now, you’ll unfortunately need to do multiple naps a day. I had to do that between months 4-6 (so post 4-month regression and before my DD’s naps lengthened), and it was seriously hard work. That period of my life nearly broke me. But slowly her naps did lengthen, and so it meant she didn’t need as many and the pressure came off a bit.
If you can get more daytime sleep, then your nighttime sleep should improve. However, one word of caution is that you might be expecting too much from nighttime sleep regardless of nap quality. I noticed you mentioned you thought he should be doing 6 hour stretches? Well, my 8-month old naps for 2.5 hours a day and is in a great routine, but she has never done 6-hour stretches at night - it’s a lot to ask from such a tiny baby. Of course some manage it, and it seems like you were lucky with your first, but 6-hours is rare. I certainly do think your DS could sleep better at night if his naps were sorted, but I would also maybe adjust your expectations of nightime sleep.
Maybe a sleep consultant could help you with a schedule for naps, but it’s often a lot of money, so if I were you, I’d try more naps for a few weeks first and see what that does. But, you do have my full sympathy as I know how hard it can be and how desperate you can feel wanting answers. The truth is that they all get there eventually, so you can be hopeful, and I think there are definitely some things you could do to help him along 