((((hugs)))) that is hard.
OK first thing is, I think he's probably a bit overtired and bedtime needs to be earlier. Like, in bed for 6, asleep for 6.30.
My daughter is the exact same age so I know how incredibly stubborn they can be. So, if he's happy, do as you have been doing and leave the room. If he calls for you, don't respond at all unless he is crying. No sleepy phrase, just leave him - just as you would leave a baby gurgling in his cot.
Also, you are going to have to expect sleep to be a long time coming. If you give up because it's 'way past bedtime', you won't get anywhere. You have to stay consistent no matter how late it gets.
So once he gets upset I would go into the room before he gets to that point of making himself sick. Say firmly something like "Oh now what's the matter! This is a lot of noise! What do you need?" Help him find his lovey and lie down.
Now this is what I do with my daughter. I say, "Honey wait there for one moment. Mama has to pee. I will be back in one moment." Then I leave the room, close the door, and IMMEDIATELY go back in. I stay with her until she's calm again. Then say, "Mama has to go wash hands. I will be back in one minute." Then go out, close the door, wait a moment longer, then go back in. After a few cycles of this she is waiting calmly for me and I can extend the amount of time each time I go out, and eventually just stay out and she falls asleep.
If he is having a tantrum about wanting to hold him to sleep, well what can I say. You are going to need to find a way to deal with it. I would pick him up and hold him until he's calm, if that is LITERALLY THE ONLY way that he will not throw up, BUT I would rock him, calm him, but all the time be saying "Sleeping in your cot sweetie. Mummy is here. I will help you. But going to sleep in your cot tonight." Just like you wouldn't give him a cookie if he was having a tantrum about it right before dinner.
How does he go to sleep for naps does this all play out the same way? I feel like bringing bedtime forward might help, it sounds a lot like OT behaviour.