the wobble problem is very very unlikely to be anything to do with the height of the saddle or the length of the stem, it’s more probably a loose headset or wheel bearing, so check those first, unless of course you’re merely trying to justify a new bike
or it could just be ‘one of those things’, i had a bike that speed wobbled at 48 miles an hour, pedal through it at 50 and it was fine, not a speed that was obtained often though so not really a problem, but a speed wobble at 30, hmmm.