OP - your baby sounds much like mine, except the sleeping from 9am to 4am part! I'd give just about anything for a night like that.
My DD is 5 months and despite a good bit of effort has never been a self settler. We feed, rock and cuddle to sleep - the alternative would mean a lot of crying and stress on her part and that's not something I'm prepared to put her through. It would also mean even less rest for me. I'm exhausted, and have been for months now, but fortunately have a very supportive partner and a DD who will take a bottle despite being bf.
There are some good tips in the No Cry Sleep Solution about feeding to sleep. Basically, you latch baby off just as they are getting drowsy but not deeply sleeping, then gently lie them down. I do this for DD - along with holding her over my shoulder for about 15 minutes after feeding (she has reflux though it's improved a little with age). We listen to some soft music, sway a bit, and I rub her back after she's laid down (she sleeps on her side - not per guidelines but necessary due to the reflux).
On a good night, she might sleep from 8pm with wakings usually around 12 and then again at 4. Often, my DH will give a bottle for the 12pm wake up, and I will feed DD lying down in bed and co-sleep with her for the 4am. It's hard. But also completely normal for a baby of DD's age.
OP, it is entirely your prerogative about how you put your baby to bed, an if you feel it is necessary to let him cry then so be it. Personally, I found shush pat bollocks, as much of the Baby Whisperer book. We tried a bit of that in the early days, but DD hadn't read the book unfortunately. Most of the methods stressed her out and just caused more crying, upset, and less sleep - and left me feeling like a rubbish mum.
No judgement here though - just saying that though your DS might be hard work at the moment, his sleep is completely normal for a young baby. He will also go through incredible changes between now and 9 months. You may have to adapt and vary your settling approaches as he grows and develops. It's good to be flexible, patient and to manage your expectations at this stage.