Hi, welcome back
I'm sure you know we won't advise any form of CIO or CC here, as it breaks the bond of trust with your child.
I think the main thing here is that your baby is getting too much day sleep and much too short A times. Really, at 7 months, a child with reasonably high sleep needs might have an A time of 3hr and you've a baby who's taking a 2hr nap 2hr after waking in the morning. Of course part of this is that he's having such a disrupted night but the way to fix that is to extend that morning A time, take him outside so he knows its day time and his body can start to regulate better.
My suggestion would be to do something like this for a week, record what happens and then search for patterns to make changes that may be required:
8 - WU
11 - nap
12:30/1 - WU
3:30/4 - nap (3hr A time here)
5:30 - WU
8:30 - asleep in bed.
If 8:30 is too late a BT, I would suggest doing this routine but shifting it back by 15min/day by waking him earlier each morning until you get to a preferred WU/BT.
He is probably horrendously OT from having such terrible nights (as I'm sure, are you). I think whilst you're doing this daytime routine, you will likely have to APOP the naps to get his body into the rhythm of napping at these times but I think once he's awake more than a 3-4 month old, he will probably sleep better at night.
Are the nights any worse since introducing solids at dinner time? if so, you can probably stop those for now - the feeling of having solids going through the digestive tract is new at first and can cause sleep disruption. Its not essential that he has 3 solids meals/day at this age.
I don't think with a routine such as what you're currently doing that its fair to try to do shush/pat or PUPD with him. You'd be expecting him to sleep when he's not tired which is probably why you're having to rock/feed to sleep. Stick with your getting to sleep methods for now and spend a week with 3hr A times, then we can tweak the routine and start any remaining sleep training that may be required. Generally once the routine is suitable for the child, the sleep training is much easier if not unnecessary.
FX we can get LO sleeping so you can sleep xx