Doing the pans and zooms in post can work – it works better, obviously, if your base shot is 4k. I do this in my ukulele concert gigs for my unattended cameras: shoot an HD wide shot, manipulate the pans and zooms in post with keyframes. It works best when the camera is super-close to begin with. Your “high up in the cheap seats” distant shot will not look as clean because even in HD, you have a limited number of pixels to blow up. A 4K recording would help.
There’s a number of things you could try regarding the tripod and technique. Some involve expense. Moving your hands off and locking/unlocking are issues. You want more spring tension and more fluid drag to start with, so you can hold the shot without using the locks. Be sure the camera is balanced to naturally return to the right level, hands-off, and you won’t spend all your muscle energy holding the shot. With a well-balanced camera and head, you only need fingertip pressures to hold a shot or initiate a move.
If the camera has LANC connection ability you want to add an aftermarket zoom controller to the arm of the pan head. Vari-Zoom controllers have a useful speed adjustment knob that can really slow down the zoom speed to a crawl. If your zoom rocker has enough sensitivity, you can use the “pinch technique” on the rocker switch instead of just pressing on it with the finger or thumb. Over the years, that’s my main technique for smooth zooms: you pinch the front and back of the rocker, the finger tips acting as drags and stoppers, and roll the entire wrist, to make the rocker move the very tiniest fraction.
Pan moves will improve with added mass on the camera and head to dampen shake, as well as with using longer arms. You may consider getting a heavier tripod and head than the camera needs, just for the stability.
I would recommend an inexpensive gopro knockoff, the iconntech, around $50 or less,
https://www.amazon.com/ICONNTECHS-Megapixel-Viewing-Waterproof-Camcorder/dp/B01F759GKC
that you locate somewhere to get a cut-away shot, and this lets you eliminate showing the beginnings and endings of your live camera moves in the edit. You could also mount it on top of the current camera, if there’s no better place. This one ugrade will seriously improve the overall professionalism of your work. If you can put a gopro or iconntech on a mic stand and get it up near the stage, …maybe hook it to the conductor’s music stand, digital pans in post from that will be amazing.
Finally, the Rode shotgun is nice, but if there’s a PA system, you should look into connecting to it with an inexpensive digital audio recorder, (used around 50 bucks for a Tascam DR-05 or similar unit) and mixing the board audio with the live “wild” sound from the shotgun. Or put the audio recorder up closer to the stage, if you can’t tap into the PA system. Poor video is more tolerable if the audio is really good. And nobody watches good video for long, if the sound sucks.