It's doable if everything goes right. Traffic shouldn't be bad at 2am when you'll be going between the two. Yes, bags take a while to get to baggage claim, but even if it takes 1 hour to get through immigration, collect bags, and customs, that leaves you 1.5 hours for transfer and get to check in counter. You have a little bit of margin, but having checked bags increases the odds that something will go wrong and eat into that margin.