I had some serious ice build-up on my icemaker:
Note the wall of ice on the back. This water would also flow into the hopper bin and freeze up, which sounds like your issue.
The dealer found the freezer door was warped, and replaced it under warranty. That helped a lot with the frost that was building up in there, but only slowed down the icing up problem, didn't solve it.
I tried adjusting the water level and that helped. Pull off the square white cover of the icemaker, and there is an adjustment screw with plus and minus markings. Turn it so the indicator moves towards the minus side. If you're overflowing the icemaker, this may help.
Turn off the icemaker (lift the wire bail arm) a few hours before hitting the road. If the ice hasn't yet frozen over in the mold, or if it cycles and re-fills, unfrozen water could slosh out of the mold and splash all over.
Later, the gears on the icemaker stripped, and I replaced the whole icemaker. That's when I made the most significant discovery. The water fill tube extends through the back of the fridge. The icemaker has a cup to catch the incoming water and funnel it into the mold. On my fridge, the fill tube didn't extend far enough into the fridge, so some of the water never made it into the catch cup, it dribbled out short of it. I put a short length of rigid tube into the flexible fill tube so that it extended out another half inch. Since then, I still need to manually de-ice the freezer, but only once or twice a season, not every month.
Here's a pic of when I had everything torn apart to replace a burned out defrost heater (the dreaded "ERR 13")
On the back wall, you can see the small electrical junction box (also visible behind the icemaker in the above picture.) Immediately below that is the fill tube - before extending it, it didn't extend beyond the sealant putty. Now it does.
Don't know how many of these issues may apply to you, maybe none, but they are some places to look. Good luck!