Exmark Lazer z won't start after trailering

So here's the issue. Ive got a early 2000's exmark lazer z 25hp air cooled mower. It has been a great machine all it's life. All of last season I experienced a major problem when ever I trailered the machine from lawn to lawn. When I would move the mower from lawn to lawn I would get ready to mow I'd turn the key and the motor would crank and crank. It doesn't make the normal noise when cranking. It pops and backfires and if you're lucky one cylinder will fire and it will run for ten seconds on one cylinder then die out. After repeating this process of getting the mower to fire on one cylinder the battery will run dead. Eventually (and I have no idea why) everything returns to normal, the motor cranking is normal and both cylinders fire and everything smooths out and it will run perfect all day long, until it is shut off and trailered again. I assume it has to be something to do with bouncing on the trailer. When it isn't trailered it will fire up every single time at my house. Possibly the carb is flooding? Or the magnetos for the spark plugs are bad? The motor was just rebuilt at the end of last season (rings, lifters, valves, push rods) and it didn't solve the problem. Again the machine runs perfect once it gets started. Where should I begin my trouble shooting? Any suggestions?