How fast is "rather quickly"? Interstates are usually the fastest, as long as there's an interstate going near where you want to be. For you, it looks like I-94 is your best way to go if burning miles is your main goal. The question is, how many miles a day can you ride? Speaking strictly for myself, 500 miles is about as much as I ever want to ride in a single day, and it's 1300 miles from Minneapolis to the Montana/Washington state line on the interstates. That's just shy of three days at my maximum pace; if you ride further in a day than I do, you'll get there quicker.
The trouble is, interstates suck on a motorcycle; when it comes to crossing big chunks of the country on an interstate, I'd rather be in a car. I've done the "Across the US" a couple times now on a bike, and as I get older, the trailering option sounds better and better. If you're going with a couple other guys you can spell each other at the wheel, and you can easily drive for a solid 12-14 hours a day.
One thing to consider besides a trailer (if you don't have access to one that can haul three bikes) is a U-haul truck. It would take some creative rigging with ratchet straps to secure three bikes in the back of one (or else you build a pallet with a wheel chock for each bike). If you can rig it with just straps, then you wouldn't even need to let the truck sit idle while you were at your destination riding; you could turn it in (and save some money), and then rent another one when you were ready for your return trip. If you wanted to palletize the bikes, you could call ahead to the U-haul drop off point and ask them if you could store your pallets there until you were ready to rent a truck for the return trip. A lot of U-haul places are attached to commercial storage businesses. With three guys sharing the driving, you could easily do 800 miles a day and still have time to get some rest at the end of the day. One added benefit to transporting bikes in a U-haul is that they're definitely secure in the back of one from theft and from the elements.
Expensive? Absolutely. It's definitely cheaper if you already have your own trailer and tow vehicle. If you're like me, you don't have access to that, so renting a truck begins to make sense.