...Any rule on how low the panel box can go? ...
Not that I know of. There is supposed to be at least 6 feet of headroom, but commercial panels are routinely placed on the floor. Those panels however are usually quite large, so most work in them would not require bending over. In a smaller residential panel, I would not want it that low.
If there is enough length to get inside above the floor, protect the exposed part with PVC conduit terminating in a 10x10 junction box. **** splices or Burndy type clamps can be used to join the conductors in the box. If you use Burndy type split bolts, make sure you follow the correct taping and leave some slack in the box.
#6 wire can be spliced with wire nuts if you get the right size, though it's not necessarily something I'd be happy with. If you want to get fancy and not use lots of tape on split bolts, there are always Polaris connectors.
The cheapest box you could put near the floor would be a disconnect switch. Those come with terminals already, so you buy one unfused disconnect rated for your ampacity, and all you'll need are cable knockout clamps.