I’ve talked to several people who have snowthorwers with friction drive (most brands do) and many have drive problems. I have a JD 928E and it also has drive problems when I try to blow snow into the wind. I just ignore it and push a bit and as things heat up the drive works better and better. Short of sealing every seam with duct tape I don’t know what a person would do to fix the problem other than to not blow into the wind.
When you say the pull cord got stuck do you mean that it wouldn’t turn over the engine when you pulled it. If so, it’s a known problem and the solution is explained on page 20 of the operator’s manual under the heading FROZEN STARTER.
As for the problems with how the engine runs after you got it back from the JD dealer, it’s likely something didn’t get adjusted properly. To replace the flywheel likely involves messing with the governor linkage, which is easy to screw up. Likely you’ll have to convince the dealer that something’s actually wrong and then hope they can actually fix it.
If you bought if from Lowes within the last 30 days then check you receipt to see if it says you can return it within 30 days. If so, you should take it back for a full refund or at least a swap with another 928E.