As you can see in videos you've provided it is possible even for more characters. In the second video you have more than 10 models, each of them is computed in realtime and I suppose they don't share the same IK results (the reason for this demo is to show it can solve foot and hand contacts for different character proportions, so each character is computed separately).
The IK itself doesn't need to be so heavy. There are many levels of IK - you can compute a hand or leg made of just two segments or you can compute entire body at once. The first one is very simple computationally while the second is almost never needed in a game.
Having that said I'm not sure if you approach the problem from the good side or I didn't understand your description. What you wrote seems like you have the current position of hand and the target position, and you want to 'drag' your character by hand from start to end.
This could work but you may end up with other problems like breaking of the rest of the body movement. Instead, I would move the character by his center as always, and IK would just respond to this movement.
I'll give you another example from Mario game:
In old Mario game you could jump under the brick to hit it with your fist but because of the character proportions its hand ended at the same level as head so it looked fine. Now let's assume you put a typical human in place of Mario.
You hit 'jump' and Mario raises his hand above head and starts moving up.
At some point Mario will touch the brick and you need to decide if it keeps moving or stops - either way may look odd.
So what can we do with IK? On jump you set simple solver, only for the raised hand. The solver have the task to not to allow the hand to move above brick level. Then when you're movig up and touch the brick then you hand will start to bend, so it never goes above the brick. Given that all the details were done right it should improve the look of you character.
On the end few random thoughts I recall from working on IK in Unity:
- Bio IK is not the fastest one, it's more like an R&D. If it works for you then fine, if it gets too slow - change it to Final IK.
- Don't drag your character by hands/feet and depend on IK where possible. Instead move the character as always and use IK only to modify limbs movement.
- Try to avoid complex IK structures, like multiple chains, full-body IK etc. If possible use few separate limb solvers.
- Final IK has A LOT of nice examples, showing you how to achieve some specific effect using simple solvers. It's worth to look at, just to see how you can solve common problems.