G.B.
He is never going to be comfortable on a baby bed mattress no matter what kind of bed you get him. Skip the toddler bed sinde he's not really going to be a toddler after his birthday. Then he's a preschooler.
I would say since he wasn't moved when he was a toddler and it's almost time to move him out of a toddler bed that is would be a waste of money.
Go for a full or queen. You don't have to spend a ton of money on a mattress and box springs. It will be big enough so that someone can actually go lay down with him to get him to sleep at first then wean him off sleeping with someone.