I also have a TI and we hardly ever use the scupper cart anymore if we are at a launch or anyplace we can back up to the water. I never put the trailer into the water, I just back it to the waters edge, then lift the front of the boat up and either pull or winch the boat onto the trailer.
Unfortunately when we go down to our key West place we can't take the trailer (no place to put or store it) so we have to car top. We usually launch at Higgs beach down there and have to cross a couple hundred feet of soft sand with the scupper cart. What I typically do is I launch the boat with the wheels in, once I'm out in waste deep water I get out and remove the cart and store it upside down in the rear scupper holes on the back deck. We sail then when we come back I stop in waste deep water and put the scupper cart back under the boat (in the water) then just roll the boat ashore. Since it is pretty difficult to drag the fully loaded boat across the sand I typically remove the AMA's and walk them up to the car separately. Pulling the hull alone thru the sand (way less weight) it's not so bad. It's only hard when the boat is fully rigged, pulling the hull alone on the scupper cart is a snap and pretty easy, and is no more difficult than pulling our old Oasis.
When on concrete ramps I try to not ram the boat into the concrete ramp (hard on the boat), what I do is just pedal up to around knee deep to waste deep water and jump out, there I pull up the rudder, mirage drives, centerboard, etc and put the scupper cart under the boat into the scupper holes. I then just roll it up to shore to the waiting car if there is some distance to go (like when we are in Key West without the trailer), or when we have the trailer I just back the trailer to the shore, then lift the bow and pull the boat onto the trailer. I have a boat winch (about $25 bucks at Harbor Freight) that I mounted to the trailer for those day when I come off the water exhausted and just don't feel like man handling the boat.
I'll be perfectly honest, I have never ever used the paddles on my boat, I always carry one on board as a backup but never used it.
You will be surprised how durable the mirage drives actually are, we seldom pull the mirage drives out when we come ashore (we have mostly sandy beaches here), we just park them up against the bottom of the hull and put the bungy onto the pedal to hold the fins against the hull. The exception being the end of the day when we plan to pull the boat from the water, then we pull the mirage drives before pulling the boat ashore.
Actually it's probably a pretty good idea not to drive the TI up onto the shore like you would a canoe, I usually stop short of shore, get out, pull what I need up (mirage drives, rudder, etc) then walk the boat up onto the shore (either with or without the scupper cart).
The TI has to be the easiest boat on the planet to sail and you will pick up everything you need to know in the first couple hrs. Keep in mind that the TI is a pedal boat first and foremost so anytime you want to maneuver you just pump on the pedals (example: going from one tack to the other). Also keep in mind that if you turn one set of pedal around backwards you can maneuver around docks and harbors easily in forward or reverse by having your passenger pedal on the reversed pedals if you need reverse (a really handy feature).
Also keep in mind in order to steer the boat has to have forward motion for the rudder to work, so even if you sail is stalled and you are in irons (you will learn what that is in the books) you can pedal your way out of anything, so don't try to be a heeman hero and try to sail the TI without the mirage drives in, the boat is designed around them and they need to be used.
Another thing that I see a lot of beginners do wrong is they go out on a fairly gusty or windy day and try to sail with the sail fully unfurled, it's fairly easy to capsize if you do that (we don't want that). One of the strongest features of the TI is you don't have to open the sails all the way, if it's kind of windy just unfurl it partially, it works just as well furled in one or two turns. Actually in higher winds (over 12 mph) you will actually go faster with the sail furled in one or two turns.
Keep in mind if the sail is over powering the boat (one of the AMA's is going under water), you need to quickly release the sail ( or turn higher into the wind (you'll learn that from the book also) to keep the boat from possibly capsizing. Though it's pretty darn difficult to capsize a TI, it will capsize if you do the wrong things in higher winds.
The TI can be sailed just as easily from either seat, and there is no right or wrong seat to sail from, everyone has their own personal preference on that, and you have complete control from either seat.
Hope this helps you