Venturing outside...

My cats have always been indoor cats as I firmly believe it is safer for them... Until now. My 4.5 year old male is severely bored inside to the point where he is causing a ton of trouble (tearing apart cupboards, knocking things over, general mayhem.)
In February be broke his paw by knocking a mirror off the wall and this led to an inflamed bladder, etc. He's on special food for it and now weighs a whopping 16 pounds; he is clinically obese.
Finally I decided to get him a harness and leash and take him out supervised with me. We went out for the first time yesterday, and then again today. And now..... He's meowing at the open screens and pawing at the door. I can't let him out alone but now I feel bad... Suggestions on what to do?

Get him a cat tree and put a bird feeder outside a window for entertainment.  Play with him using a laser toy and interactive toys like DaBird.  All of this "mayhem" is normal behavior for a kitty who wants attention.  He needs stimulation, not necessarily the dangers of outside life. 

They have several cat trees and are played with at any given one between my 4 year old stepdaughter and I. He is ONLY going out while in a harness with me and exploring the backyard for like half an hour at a time. We have double doors to a sunroom and I have microchip vouchers for both cats; it's literally my worst fear that something happens and they get outside unsupervised. My other cat isn't interested in going out.