Not familiar with Honda but it sounds like a carb problem. Could have some trash in float bowl or float could be sticking. Think first thing I would do is run a good dose of Stabill through it and see if it clears up. I have found usually a glommed up low speed jet causes that dying when put in gear. Also float level can effect it. Like if there is some gum on float shaft it might not open all the way. Don't go messing with adjustments. If nothing came loose or broke and it ran good before that's not your problem. You say you have new plugs, my 50 yamaha did that and I found a bad plug. Could never tell it was bad the way the motor ran except when loading on trailer.