Sounds like he isn't tired when you want him to have a day sleep. Give up on it. Especially if he sleeps well at night.

I found the pram was great for a non sleeper: either he was awake and enjoying the fresh air, or he'd drift off after half an hour. I would sit him up slightly too, helped with his tum. Then he wouldn't be strapped to me so I could have a coffee and read. I mean do the washing, of course.

Eta do you let him cry alone, or do you hold him? I worried when you said "professional" help, as I know what that was like for me. Some babies will never cry to sleep, no matter what you were promised. The ones who give no cues are more like that than others. I had one like that too, and at 7 he still gives no cues!