3 year olds need about 12 hours of sleep a day. Sounds like maybe he's OT? I know my daughter just started nap refusals a couple weeks back, it was short-lived, but I ended up looking up how much sleep toddlers etc. need and read that 2 year olds need 13 hours, while 3 year olds need 12.
I would definitely suggest EBT of 6pm so that you're getting 12 hour days.