I wish I could help, that sounds utterly exhausting and you have my full empathy. I feel very new to this too, I have used an Amby baby hammock for a few months and found that great but I am transitioning dd who is 5 1\2 months to a cot at the mo and finding her sleep patterns have changed, you could try him in an Amby, I got mine 2nd hand on ebay for £80, they are expensive new but they do travel well and they gave me stretches of 5 hrs from 7.30-12.30 then she slept till 5am for months, then she would usually need to be in with me and fed to sleep, now she is on 3 hrly cycles and wake ups sometimes at 3 or 4 am for 2 hrs then a short nap then up for the day, hard work...
You can 'snipe' auctions so you don't have to be there at the allotted time to win the item, something that is virtually impossible as a single parent, I am with auction sniper, once I got my head round it (not easy when you are tired I must admit) I started winning loads of things I needed, I recommend the group feature where you can set your price on an item, put it in a group and they bid on each item as it comes up until you win one then it cancels the group, makes more sense on their help page...
www.auctionsniper.com/
I figured I could always sell the Amby on ebay if it didn't work for my LO but it did and I may keep using it for daytime naps and time away once she has settled in a cot.
Someone recommended a woombie which I am looking into, its like a swaddle but more flexible, it stops the startle reflex and gives them a cozy feeling...
I hope that helps, and you are able to get some rest soon, is there anyone could be with him whilst you nap in the afternoon? I find a long nap a couple of afternoons a week really saves my sanity and charges up my batteries,
best of luck to you, it sounds like you are doing all the right things and he just needs a little more pursuasion to get longer shuteye,
xx :)