if it's 'dieseling' ...running on, in any gear there is a problem. 99.9% related to ignition timing. slightly too advanced, possibly too much vacuum advance. i'd look at idle speed, initial timing, vacuum advance and total advance to find out where it is when this is happening. make sure to make all your checks and corrections at full operating temp as i would assume it probably doesn't do that if you just start it up, pull it out of the garage and shut it down in park. just my assumption, correct me if i'm wrong, but it probably doesn't start the run-on effect until its hot. there are a lot of variables that could come into play but it all ALWAYS starts with ignition timing. poor fuel quality, too much compression etc etc can all contribute but most can be rectified with proper ignition timing. I'm going to guess that you probably notice a huge difference in idle speed between park and a drive gear. this is also likely related to ignition timing first and then fine tuning of the carb second.
you state that you're not too mechanically inclined when it comes to engines so i would find reputable shop that you trust and have them go through the timing and carb tuning. you may be surprised to have a completely different ride in all aspects, not just shut down.
just my opinion