From what you say it looks like when your engine was last installed the mount feet weren’t properly shimmed. Basically the engine should ride in the middle or lower part of the stud that comes off the mount. If, to align it, the engine is on the top of the mount’s stud you put some material under the feet of the mount to raise it up so the engine rides lower on the stud.
If you’re engine is running smoothly there’s no urgency to correcting this. Give it’s the beginning of the summer I’d wait. You never know what rats will crawl out of the woodpile when you start taking your engine apart.
I’d be concerned about and fix the exhaust system issue . The exhaust hoses should take up the vibration and the mounts should be secure. A hose failure and the leaking of CO and water into the boat is a big problem.
It’s not too likely that the other mount is too low because of degraded rubber. It’s probably low because that’s where it had to be on the stud to align the engine to the shaft. The engine lets you know when the mount’s rubber deteriorates to the point they need to be replaced. Usually mounts only get changed out when doing a major engine overhaul or replacement. They just don’t wear out.
If the nuts are loose, tighten the upper ones. Since the engine rides on the lower ones this won’t affect the alignment. If you change the position of the lower nuts you’ll have to realign the engine.
Pulling an engine or jacking it up to replace the mounts waterborne shouldn’t be a problem. I’ve done it ok. In fact it’s preferable to align the engine to the shaft waterborne as the hull flex is different when the boat’s out of the water. If you’re disconnecting the shaft from its flange waterborne you need some hose clamps on the shaft so it doesn’t slide out the stern tube by mistake
Engine alignment takes preparation and a lot of patience. Read up on it beforehand. Too much to address here. You may want to talk to a marine mechanic about shimming and aligning the engine if its not running smoothly.