I'm sure that there will be many different perspectives here. For context, I learned to play on a borrowed late '60s Mustang many decades ago, then played long-scales exclusively for three decades, moved to a combination of short and long-scales about 15 years ago, and have gradually drifted to short-scale almost exclusively. Age, reach and back pain have influenced the decision. Whilst short-scale basses can be heavy (I have two very heavy shorties), overall I they tend to be a lighter. On the questions:
1. In my case, a very long time indeed. However, I played both for an extended period (and still use a couple of headless 34" scale basses). I didn't really notice the transition or any problems. With fairly regular use, I wouldn't have thought that the shift would take longer than a couple of weeks (though it depends on the individual, of course, and possibly the bass?)
2. There is a vast range of shorties available - more seem to pop-up every month. Some of the more vintage shapes do seem to feature a bit of compression in the body - the shorter top horn can affect balance. However, many designs balance beautifully in my experience. I have a Wilcock and that is possibly to most beautifully balanced bass I've played - it's genuinely remarkable. The same is true with Spector shorties (the balance is much better than long-scale Spectors for me). So, it's worth shopping around and consideration of where the strap pin sits with respect to the 12th fret - a massive generalisation but a useful rule of thumb. It's also worth thinking about the placement of the bridge (back-end of the body?)
3. You also mention tone/sound - there's a perception that short-scales tend to be a bit thumpy/dull. I think this it true of some models, but others are very different and some can be extremely bright and pokey. I have a Spector that is capable of sounding very bright and alive. Alembics are weird full stop, and the shorties, whilst they are capable of the characteristic piano tone, sound more like an upright than a grand piano to me. That said, an enormous range of tones is possible with the filter electronics. The small-bodied shorties are a nightmare on a strap - again, bridge and strap pin placement.
So in sum, probably worth taking a really good look around and trying a wide range of shorties - the variety in balance, tone, weight etc. is enormous, and I'm sure that there's something in the mix to which you could adapt fairly readily