I am not all that familiar with various allergies or infant milk formulas but if your LO is intolerant or has an allergy to cows milk protein then the goat milk formula is not likely to be a suitable substitute - have you discussed this with your paediatrician? It's just that I see on the NHS (UK) website that goats milk formula is not suitable for LOs with a cows milk protein allergy.
With the naps being so difficult and so short I do wonder if there is still discomfort - do you feel the reflux or any allergy is under control fully?
Here's info on W2S, see naps option 1 as you do not actually wake baby up.
https://babywhispererforums.com/index.php?topic=223809.0It's worth a try for a few days.
Should I wake him in the future? He's just fine doen with a cough and cold so I felt he needed the sleep?
Sometimes the day is thrown off by a late wake up but if LO is poorly and you feel he needs the sleep then I'd probably let him sleep and prepare yourself for whatever happens next, expecting the day to be off track. If it was a regular thing waking late in the morning I'd suggest looking again at routine and perhaps deciding on a morning WU time to get things more consistent.
In the night he often stirs and can go back to sleep on his own so I think he can transition between cycles?
night sleep is a different skill to day sleep so although it's a step in the right direction being able to transition between cycles at night is not the same as learning to do so in the day. W2S is one method of teaching him this skill and habit to stay asleep.
I do think though that perhaps another chat with the doc/paedi might be needed.
How many doses of ranitidine per day is he having?
What's his weight now?