At Terminal 1 at least (I think that's where Delta is), the closest you can get to the baggage carousel is about 250-400 feet, depending which carousel. You have to walk to the exit door, then traverse a walkway to the pickup lane. The pickup lane is immediately next to short-term parking, which I think is free for 15 minutes and $2-3 an hour thereafter.

They have SmarteCarts outside by the curb. They also have free luggage carts at the rental car facility.

I see you as having two options: 1) go outside and get a cart, get your bags, take then to the rental car bus and get them on and off the bus manually, when you get them off find a cart and you can keep the cart through the rental car line and take them down to where you get your car.

2) Go pick up the car and drive back and park in short-term parking. Get a cart and get your bags from the baggage office, take them back out to the parking, put them in your car, then return the cart.

I would opt for #1 since the only additional effort is getting the bags on and off the bus, and it will probably save you a fair amount of time.