I looked at pics of your type of van, and it's not what I imagined (I was imagining like an econoline van or something (really tall) in my mind (I don't do foreign cars).
I see no reason you couldn't get the TI onto the roof for transport, it's actually not hard to get up there since you only ever lift half the hull at any time (around 50 lbs). With the setup in the pics below we have a couple hundred thousand road miles with the kayaks on the roofs of our vehicles (we are campers and use to tow our camper around the country so the trailer hitch was occupied (we actually wore out 2 Yukon Denali's doing this), and are near end of life on our third one).
Just for transporting the boat home you might not need the T-bar hitch (requires a reciever on the vehicle) if you only going to car top once or twice. The Tbars have 500 lbs capacity and support the bulk of the weight of the boat, so on long trips, they are pretty nice, and give me a feeling of added security.
You will need some scrap carpeting (to insure you don't scratch the roof). I would bring along 5 or 6 foam pool noodles (they cost like a buck apiece at Walmart) and you stuff them under the boat to even out the load. You will also need about 4 1 inch wide x 15 ft long cargo straps (to strap the boat and AMA's down to the roof). I would also take some additional strapping or rope along so you can strap the bow down at the front in a V shape to prevent the vow from waving side to side.
Take everything out of the hull including all seats, AKA bars to get it as light as possible. All the pieces get stuffed into the back of the van before putting the boat up there typically.
We have the T-bar (about $80 bucks from Amazon), If I was going to order a new one I would definately order the type that tilts down next time around. You don't have to have the T-bar if your only doing one time.... (that's what the scrap carpeting is for)
You can see the front straps in this pic.
The procedure is place the hull only on the ground behind the car with the rear of the hull centered in the middle directly behind the car sitting on a piece of scrap carpet. Place the front of the boat with bow along side the car about even with the rear wheels of the car.( the boat is at an angle). Now you place another piece of carpet onto the roof near the rear of the car (the boat will sit on that). You now lift the bow over your head (your only lifting half the weight (around 50 lbs), so it's not that hard (get help if you need it, I'm a small guy and have never needed help the thousand times or so I've done it). With the boat kind of on your head walk back hand over hand so you are behind the car. Now walk sideways and place the bow of the boat in the center of the roof (on the carpet). If you have a helper, they can steady the boat so it doesn't go sideways on you (I never needed anyone). Now you walk back to the back of the boat lift it up and start sliding it forward. I usually roll mine on the pool noodles (makes it easier to roll). Keep on pushing forward until the boat is where you want it. You may need a pool noodle over the drivers seat area to prevent the boat from tilting forward. Now just start stuffing in pool noodles everywhere you can find to even out the load on the roof. Now you shove you sail (in the bag) along side the hull (close). Next you throw the AMA's on the roof one on each side of the boat. With ours the spacing is perfect and the roof rack traps the boat and AMA's from moving side to side. Now strap the whole works down with multiple straps. If you have something similar to my pic below for the bow you should be ok (all those straps I have are 800 lb min, nylon cargo straps).
If your not doing the T-bar thingy, you will need to do the same strap thing on the back of the boat. If the back of the boat is more than 4 ft behind the bumper, you might want to hang a red flag back there (optional but probably not neccessary), we have never been stopped, and have been in most of the states.
I wouldn't recommend trying to put the boat up there upside down, you will wreck your car. When we are in Key West (where there is no parking, and any parking is very expensive, and there are two trailer parking spaces on the whole island at Simonton st launch ($2.75/hr just for the trailer, then $2.75/hr for your car on top of that). We just keep the kayak on the roof for up to a month at a time, then take it down daily when we want to go out. We have motorcycle locks to lock the hull and AMA's down to the car roof rack. Besides, the TI has an automatic theft deterrent system designed in at the factory (it's 18.5 ft long and not very light, I just can't see two teenagers running down Duval st with one of these on their heads ( lol) just sayin.
Another big deal is our boat is titled and registered (at the advise of our insurance), it's an automatic grand theft felony (like stealing a car) if stolen, anyone with any brains realizes this.
Getting the boat up and down from the roof is actually the minor part (just takes a few minutes), it's all the rigging, putting the seats in, lacing the tramps, putting the AKA bars in, etc that takes about an hour for us, but I have massive sails (260 sq ft), outboards, etc on mine (way more crap). When we can use our $140 harbor freight trailer, we do, it just takes 15 minutes to launch, plus we store the boat fully rigged in our garage, nothing is ever removed from the boat. When done sailing locally in Sarasota we pull the car in the drive rinse the boat off, and pull into the garage (takes all of two minutes).
This is the trailer setup we use when we don't have to car top (much preferred)
Good luck
Bob