Back in the day I could hit the ball a mile! Played near a scratch handicap. Also walked and carried a lightweight stand bag for many year despite an ACL reconstruction on my right knee, and MCL sprain in my left, various and sundry ankle breaks and sprains, and a left shoulder separation. But, after some time, my knees informed me that they no longer liked that!
So, I bought a pull cart. Played that way for quite a few years, until my knees started talking to me again! I fought against it for years until a 9 hole round of league golf would have me in pain for much of the week made me decide to ride in a cart!
You have to deal with reality!
A bit off topic but I believe the extended tee times both separate groups but also limit the number of carts on the course. 15 minute splits puts a maximum of 16 carts on the course per hour and a total of 64 maximum in 4 hours. Many of our local courses only have about 60 carts so to keep carts available to the groups later in the day, they limit how many go out.
As to all the games that are being played at @FlyingAce's private club, I might seek out similarly affected members and go as a group to the head pro. Present a series of reasonable changes you would like to see instituted. Give the pro a chance to make things right. If he ignores your reasonable requests, it might be time to find a new club.