New to the Spyder culture, been 5 weeks since I bought my 2014 RT LE with 9100 Kms on the clock. My friend started me down this road when he sold all his two wheels which he is slowly replacing with different make/models, and bought a 2018 F3 Limited. Still have my '85 Honda Goldwing Limited Edition to satisfy the 2 wheel riding - sold my 1500 Goldwing when I bought the Spyder.
My friend had his 2018 serviced and needed someone to drive his truck once he picked up his Spyder. Unbeknownst to me, he organized a demo day for me, a 2020 RT LE. Went out for a couple of hours and it wallowed in the corners, no upgraded sway bar. My 2014 has BajaRon's sway bar and it makes a serious difference.
Raised and lived in the snow regions, and quickly learned that the riding a Spyder is similar to riding a snowmobile. Since you have not had this luxury, a two wheel advance riding course, or track day to learn how to hang out the side of a bike is beneficial. Slide to the inside of the corner, hang your butt and leg out there, and cornering will become easier - motorcycle racers do this well and it allows them to go faster through the corners. After a while you will get the hang of properly entering a corner to minimize the effect of the corner on you, speed - entry/exit point, same as a two wheel.
I still want to corner much like on a two wheel in that I want to keep my body in line with the bike. I think it's because I have the visual concept that I look foolish hanging out the side of the Spyder in a corner. Will get past this.
Three wheel trike concept like the Spyder is not a new concept. Late '60s/early '70s there was a summer bolt on kit for snowmobiles. Install wheels where the skis were and a sprocket on the drive shaft with a chain to a rear wheel. Not many around back then, but these kits were available.
I have been riding my friends 2018 F3 intermittently over the past couple of weeks and find there is a considerable difference in the "feel" of the machine especially in the corners. Had a friend follow me today and I asked him to comment on the lean of my 2014 RT LE on a couple of cloverleafs we had to go round. He mentioned that the Spyder did not appear to lean at all, but the sensation felt was the opposite.
Another technique to try is to brace the leg that is relative to the turn/corner - left turn/left leg, same for a right turn. This stabilizes the lower body. After this, lean into the turn as appropriate so that you are comfortable. You can also use the arm that is opposite to the corner being negotiated to stabilize your upper body. To steer through a left handed corner use the right arm and hand to do most of the steering through the corner - push and relax as required to accommodate, helps stabilize the upper body and can assist in how much you want to hang out the side of the Spyder.
When you mention a lateral movement I'm thinking side to side. The road could be the culprit, lots of rutting from traffic. Since the Spyder needs to be more towards the centre of the road, the rear wheel can be on a high point and the front tires in the ruts. Doesn't take much to move either way when something occurs, trucks passing/gust of wind and such. You wouldn't use a death grip on a car steering wheel if this happened, don't have to on the Spyder. My Goldwing has a bad habit of going from side to side in my lane when I'm riding unless I concentrate on what I'm doing, but I let it go and enjoy the ride. Boating is the same. See lots of boats doing a zigzag dance instead of going in straight line. Fixated on what is close instead of fixing their sites on a more distant item. Lots of similarities with various forms of transportation.
We're taught on a two wheel, or any other vehicle to not fixate on what is immediately in front of you, look down the road. Same with the Spyder, it will go where you look. I used to groom snowmobile trails with a tracked groomer. When I started I was all over the place, too much seeing what was close to me. Adjusted where I looked, much further down the trail and I started to do a good straight trail groom. Same principle.
The Spyder RT LE has a higher centre of gravity than an F3. Notice this more after I ride an F3. Nature of the beast.
As has been mentioned, it will take time to adjust to the nuances of the Spyder. Keep to the posted speed limits to start, and the recommended corner speeds. It takes time to get used to it, and your background is instrumental in this. When I started riding a 750 cc bike was a monster, I bought a 250cc. My father was with me and mentioned that I should really buy the 750 - a Suzuki "Water Buffalo". I mentioned that it was too big, some 4 months later wished I had listened.
Shifting is a personal issue. Don't let others influence your decision on how to shift, just don't lug the engine. I like to stay above 3000 RPM for shifting and riding in any gear, similar to my '85 Goldwing. Shifting is also dependent on how I feel. If I am alone, not two up and want to play a bit - more RPMs before shifting. If I feel lazy, closer to 3000 RPM. There is no right/wrong with this.
There are a lot of similarities between riding a Spyder and a two wheel, just have to realize that the Spyder itself acts more like a snowmobile/car in that it leans away from the corner instead of into it and adjust for this. On a straight stretch, it's the same.
Not a lot of videos on riding a Spyder, but there are a lot of videos about riding an ATV 4 wheeler. Watch a few especially those relating to sand dunes and going through the bush. Watch how the rider counteracts how the ATV is behaving. Might find a video or two on instructional techniques for different riding conditions and apply these to riding a Spyder.
Having mentioned the above, and it is a bit long, don't let your two issues be a basis for not buying a Spyder. Had the same trepidation when I got my 1800 Goldwing several years back (now sold). Took some courses facilitated by instructors that rode and instructed on their 1800 Goldwings. After the first course, noticed that the "beast" of an 1800 Goldwing now did what I wanted and not the other way round.
Buy the Spyder and enjoy the ride. You won't regret it.
Cheers