Engine 20 hp Kohler Courage hard to start.

I bought this mower used. It was one year old [a 2011] and had been used maybe 25 hours. It provided me a summer of good use while I was deciding what zero turn I wanted to replace my Gravely ZT with. I knew it would not be another Gravely. The second summer I used it for rough area mowing and towing the yard trailer around. It began to hesitate while starting and I took to tapping the starter lightly to get it started. Finally would not start at all. This winter I brought it inside the shop for servicing and a new starter. The new starter was no better than the old one when it first began to hesitate. I checked all electrical connections and battery cables, all good. I went to Oreilly Auto and bought the largest cranking power battery they had. No improvement. I checked the valve adjustment and found them to be at factory settings, 05 on int and 07 on exh. I reset exhaust to 05 as was suggested on another site. No change. I pulled the head and looked for anything but all was as new. I pulled the case cover and looked at cam gears and ACR, all as new as far as I can tell. I have ordered a new exhaust cam assembly because it is the only thing I can think of to do. Anyone have any suggestions otherwise? Thanks.