So bizarre -- I just posted about this, but as it relates to a collapsed trachea. Your Max may have a collapsed trachea to some degree. I just learned (like in the last 24 hours) that using a gentle leader harness is a HUGE help to prevent the choking. Alex will even choke/goose honk with a regular harness, including the really nice ones that have chest padding. Because they still go around his neck to some degree, he ends up choking with even the slightest pressure on his neck.
I just bought this today (
Easy Walk Harness Product Description - Premier Pet). I got the Premier Eco Easy Walk Harness and leash set. Works awesome!! We just got back from a long walk and not once did he honk/choke. Now, most people use it with the leash hook in the front, but I just turned it around so that the leash loop is on his back. Still works great and puts absolutely NO pressure on his neck (all the pressure is on his rib cage).