It’s a zero turn with a 5’ deck. If I’m understanding the link they are talking about walk behinds? I never did see any pics or video demonstration, so maybe I’m not fully understanding.
With it being a zero turn, these things will pivot nice and sharp. Can you pull up to the door somewhat sideways, maneuver one side of the deck through the door, pivot a bit, and get the other side through?
For example you pull up with the left side of the mower to the door, turn left enough to get the left end of the deck to cross the threshold, pull forward to straighten out, back up and put the back corner where the deck meets the chassis against the door jamb, then slowly pivot the rest through the door?