Hugs I know how you feel, toddler plus non-sleeping baby =
Personally I would pick a day when you feel ready and go for it, naps and nights all at the same time using PUPD. Yes it will be quite a painful couple of days but really you should see some rapid progress at this age, and if you've been sleep training for naps he will likely be shattered so in some ways bedtime should be easier as he will be tired out and not able to fight it for so long. Make sure you read all the FAQs on the PUPD board before you get going. For naps you try for 45 mins and then take a break, some A time before trying again with next nap. At bedtime and NWs you do it as long as it takes.
A couple of things you could do in preparation though -
Gentle Removal Plan I know one Mum here used this in combination with PUPD and successfully got her LO sleeping in the cot. You could also work on spacing night feeds to no more frequently than every 4h and use whatever other means to settle in between. If it's a 'feed' waking once you start PUPD then feed immediately, it's ok if that happens to be feeding to sleep. If however it's a 'not feed' waking you should see it through until he sleeps, even if that takes you past feed time. Does that make sense?
Could you just clarify how many times/when you are feeding him in the daytime? I can only see four feeds on the routine you posted which is totally normal, but elsewhere you mentioned feeding 2.5hrly? I'm guessing some of the issue with him not being interested in solids could be due to having so much milk so not actually hungry.