With regards to the F-Type, I wouldn't try the back foot first. Here is what I recommend: Try starting with the front foot in the strap *before* you are planing. You can even be hooked in if you want. Have the back foot over the centerline for keeping the board flat, and also when you push sideways on that back foot it will give you lift on the fin to help get the board planing. Bear off and weight the harness and if you have power you will get planing. A catapult occurs when the Center of Effort in the sail gets significantly windward of the centerline on the plane of the sail and/or significantly forward of the Center of Lateral Resistance. As you get on a plane the center of lateral resistance moves back, with much less of the board touching the water, and you have to sheet in to compensate with the apparent wind moving forward. So you head a little downwind to get powered up and get planing, but once that process starts you need to be ready to rake the sail back and sheet in. I am sure you know all this, but the point is a catapult occurs when you do not react properly to those rapid changes in the forces going on.
I suggest trying starting front foot in the strap and hooked in on a beam reach, rig pretty vertical, and go a bit downwind with a gust to power up. Focus on weighting the harness and pivoting the body to sheet in, as you rake the sail back as well, as you get on plane. Focus on feeling the balance of everything and getting solid mast base pressure, and making sure the COE of the sail doesn't get out of balance with the centerline on the plane of the sail, and with relationship to the CLR fore to aft. It sounds complex, but once I started thinking about it in that way, and learned to feel those forces, the catapults went away almost completely, very quickly. If you have weight in the harness and balanced power, getting the back foot in should not be scary. You can slide the back foot out to the rail and then lift it to step in, or even do a double pivot to slide it in from there. At that moment where you are about to pick it up, put some extra downforce on that boom and you will be able to pick that foot up and hold it there in the air for a couple of seconds if you want.
Good luck with that, once you get control with both feet in the straps, you will "tame that beast" and love the F-Type. My favorite setup was with an 8.5 with the 148. With 7.5, the sea state starts to get such that there is enough chop you want to get off that thing quickly (if you want to keep your fillings in your teeth), unless you are lucky like Roger to sail on the sound side in Hatteras where you can get good winds and flat water.
I loved learning on the F-Type, but now I think it is kind of a weird "tweener" board that would no longer fit in my quiver. If I want wide for early planing in light winds and flat water, I go to the extreme of a Formula board (and soon the ultimate extreme of the Apollo) with a wider tail and a longer fin. From there I jump to 75-85 cm slalom boards, which handle chop a lot better and are a little more lively to sail (and jibe) than an F-Type, and still plane pretty early. Of course I am lucky enough to have committed myself to a 5 board quiver, so for me that makes sense, for others aiming for a 2-3 board quiver, maybe not.
As for your Carve, it is actually a bit shorter than the Sharks, but that's okay, you will get used to it. Tip for the Carve for you (I had the 122), get it planing solid before trying to weight that back foot, it needs good speed and waterflow over the fin before trying to get in that backstrap, or you will quickly sink the tail and/or spin out. And yes, you will round up and go sideways if you have you weight in the wrong place. You need to be tight on the centerline, front foot forward, and body twisted with sail raked much more forward that schlogging on an F-Type. The geometry and physics are much different, that is why I jumped in on this thread here with you, I went through the same challenges coming from learning on the F-Type trying to get to smaller boards. But I can happily say I am now easily planing on the 61 cm wide 95L freeride, with 5.0 and 5.5 sails. My strength is still the bigger wider slaloms and Formulas with sails 6.5 to 10.0, as those are the conditions I sail in the most, but now at least when it is ripping I can get out there, have some fun, and try to continue to improve the skills needed for those windier conditions with smaller gear.
Best of luck!