HI T.,
I just moved my son to a toddler bed but he is much younger than your son, 20 months! I decided it was time because he kept trying to hike his leg up over the side and I thought it was only a matter of time before he got out and hurt himself.
I do not have a baby gate at his door nor do I lock it at night. If he wakes up in the night, he comes into our room (if I don't make it to him first). I still have the monitor so I can hear him when he opens his bedroom door. I do have to say that he is sleeping better through the night since we transitioned to the toddler bed (knock on wood).
We were actually on vacation for two weeks and when we came home we made the switch then. He was really excited about it. It's been about two weeks now and the excitement has worn down some, which I am happy about since it was keeping him awake longer.
I'm not sure how you put your son to sleep now, but we read stories and then I turn off the light and pat his back or just sit with him until he falls asleep. Naps seem to take much longer to get him down but I most days I run errands in the morning and he passes out in the car on the way home. When he wakes up from his nap he just walks out of his room and greets me in the livingroom.
If you are insisting that your son at least have quiet time then I think you should get a baby gate. Or I saw one mom suggested putting a baby door knob lock on the inside so he can't open the door himself, but it's not locked.
Good luck!