Sometimes when kids are overwhelmed by change (either developmentally their own change, or family changes like the baby), I also find that giving them FEWER choices helps a lot. Making decisions requires some emotional effort, and when they're emotionally on edge, sometimes a decision might be the thing that tips them over the edge.
A couple of things struck me in your post: You warn, and then you warn again, and (reading between the lines), you warn again? It's a perfect set-up for letting him know that you don't really mean it.
Also, are you expecting him to do all of this on his own? My kids both needed my help in getting dressed until they were 5 1/2, maybe closer to 6. Not because they couldn't get their clothes on, but because they needed me to help keep them focused, and they liked the attention. Even now, when my 7 year old has trouble getting moving the AM, if I tell her to bring her clothes in and get dressed with me, it goes better.
My advice would actually be a mixture of focusing on connection and a clearer routine with clearer boundaries.
1. Give him one-on-one time for about 30 minutes every day. During this one-on-one time he leads the play. You're the follower. You take part, but he's the director. This time connecting really helps my kids (even though they're now 7 and 10 1/2). I find that little things I ask them to do go much more smoothly if they've had the connection time.
2. The kitchen timer, as others have suggested, makes a really good 'neutral' party. We still use the kitchen timer. "When the timer beeps, it's going to be time to..." My kids have even turned the tables on me and when I've said "I can play with you in 10 minutes," they go set the timer. (They know me well enough to know that 10 minutes soon stretches on to 15 or 20.)
3. When the timer beeps, it's time. Period. No more warnings. If you need to escort him to get dressed, you do so. If you need to sit down to eat, you do so. If you need to leave the house, you leave, whether or not he's dressed. Preschool teachers have seen more than one child in pajamas during the day. (You might want to warn them that this might happen.)
4. A routine really does help. A visual routine often helps. Another trick is to ask him what comes next? If he has a routine and knows it, this somehow gives him more ownership over the steps. (At least that's my theory, because it works with my kids.) The routine needs to be the same every day.
You might also consider mixing things up too. Can he go to bed in his school clothes? Eat peanut butter on toast in the car?