Yes, it seems like there is a real opportunity here for someone who is handy at metalwork and motivated for product development. Imagine a standard Trax-2 type scupper cart design. Bend the vertical axel support pipes further out so that they extend beyond the sides of the PA when mounted in any scuppers. That way, the cart could accommodate large diameter wheels without rubbing on the hull. Use an axel and appropriate hardware so that you could quickly swap out one set of wheels for another (soft urethane Wheeleez style for beach, Heavy Duty Foam wheels for concrete or hardpack, inflatable, solid, etc for other conditions; various diameters from 24 - 42 cm). All of these wheels would fit on the same axel and none would rub the hull. Buy the scupper frame with whichever combination of wheels work for the areas you launch. No need for different carts for different conditions, just pop on a different set of wheels. The cart would have to be left onshore, but I think a lot of people leave their cart at the launch point most of the time, anyway. Just an idea...
The wider cart can easily be made with 1 inch stainless boat rail tubing and a cheap conduit bender from Home Depot. Use the rail hardware to put in the cross brace and don't rely on the little 1/4-28 set screws, and instead use through bolts in those holes. You can drill the tubes for an axle to fit the hubs you choose. Be sure to put braces from the middle of the axle to the junction of the uprights and the cross brace. That will help to keep it from deflecting a lot and having the wheels tip in at the top. They will do enough of that anyway on a long axle. Triangles are your friends in structures.
Turn the cart upside down and stick the uprights in the scuppers from the top. That is how I kept the cart with the boat when I had the scupper cart.
I believe the OP is interested in not having the scupper style cart. Water deep enough to stuff the cart in from the bottom without tipping it on it's side is going to be a very cold affair in most Michigan lakes. Much better to shove it off in water just deep enough to float the Yak with the rudder up and the drive out.
And yes larger diameter is great until you take the OPs original intent again. The larger the diameter the higher the cart is. The higher the cart the more difficult it is to load the Yak by sliding on. Been there done that and bought the Tee Shirt.
Hobie PA14 with a mod or twoSome random Modification Pictures