sorry to hear your Ds was poorly
I would continue with HTTJ if it is working for now - you don't want to get in to the habit of doing it every single day but just try to hold off every 4th day to see what happens and see if he can transition alone. TBH when mine dropped to 1 nap (obviously older than your LO is now) and I used W2S I did do it every day as I could see it was the only way to keep him asleep and get the one good nap, I went on far longer than the 3-4 day cycles because I just knew he'd wake too early if I stopped. it became apparent when he was ready to get through alone again. The method though isn't *supposed* to be every single day.
I am not sure exactly how old your LO is, late 5 months, approaching 6 months I would guess so the chances are that the A time is getting too short again.
For late 5 months early 6 month you're looking at 2hr 30 to 3hr A times. At around 6 months usually closer to 3hrs and LO drops from 3 naps to 2 (the CN is dropped). With that in mind I would keep all A times at least 2hr 15 and suggest increasing the first and second A times to 2hr 30. You might need another increase over the next couple of weeks to 2hr 45 or even 3hr. Move in 15 min increments and always wait a few days for LO to settle into the routine before increasing again.
One other thing you could try is to go in a second time on nap 1 and see if you can get a third sleep cycle making a 2hr nap. If you can't get that third cycle then no harm done, I wouldn't try for a long time to resettle if it causes crying etc, I just think it's worth a go to see if that nap can be longer.
It's a pain when there are external noises etc to add into the equation. I would help him transition if you know there is noise etc. Maybe white noise or music would help cover the irregular work noises?