Speedline Models is producing a 1/16th LCM3. Should be available in February.
The LCM3 did carry the Sherman but there was also a purpose built verison of the LCM3 called LCM6. It was a LCM3 with 6ft added to the rear end of the loading bay just to increase the carrying capacity.
If you are looking for 1/35 scale kits I recommend the Revell one. During my research for the project I bought the Trumpeter kit, the Revell kit and the Italieri kit. Non of them actually have the ramp raising method correct and all are very different in many area but Revell’s is very nice and you get a Jeep and trailer to go with it!
If you want to scratch build one Chris, I can email you some drawings I made for the LCM3 and a an LCM6.
Adrian Gosling