I tried that method, but the spot that I mostly launch from is a gently sloping beach so
there's no way I can have the bow on the beach and the rear of the yak in enough water
to insert the cart.
When there are choppy, onshore waves, this would makes things even more difficult.
The simplest way (I was sceptical at first) is to haul the lump out of the water, fold in the
amas and bungee them against the hull, then (while holding the cart in one hand) tip
the yak on its side using one of the side handles. Once it's at about 70 degrees, simply
slide the cart into the scuppers and gently low the yak upright again.
I usually remove the mast/sail, but I've seen it done with the mast still in. It does require
a little bit of arm strength, but after a few goes I found it quick and relatively easy.
I generally use this method too when I'm launching and landing in surf zones.
The only thing I dislike is that it puts a lot of pressure on one scupper hole and also has the potential for damaging the soft wheels/hubs.
If you use this method, lock the scupper cart in place first, and be as gentle as you can when transferring to boats weight to/from its side.