You are stuck on thinking you need a 60T axle sprocket. YOU DON'T . . .
Another way to go about this is to run your plate mounted T/C to drive a jackshaft
to help change your ratios.
You say you have a 14T at the crank and a 37T on the axle - OK, a 2.64 ratio.
Personally, I'd:
(Assuming you are going to run the 40 series T/C that came with 10+12T sprockets)
Run the 12T on the T/C driven shaft to a jackshaft with a 28T = 2.33:1 initial ratio.
Then use a 12T on the output end of the jackshaft to drive your 37T
on the axle equals another 3.08:1 - compounding the ratios to a 7.17:1 ratio.
With the weight of the cart, you will like the extra gear ratio.
Probably slightly more cost, and some fab skills involved, but the end result is a setup
that has a tremendously broadened ratio selection. You can easily manipulate the ratio
by swapping jackshaft sprockets.
Added advantage is that you have more ground clearance with the 37T axle sprocket,
minimizing the possibility of ground contact damage.