Cutting depth of a Jig Saw
Hand-held jigsaws are not the right tool for cutting large notches in a 6x6 post. Yes, the blade must extend past the wood - they only cut on the front of the blade, not the bottom. And the blade will drift quite a bit going through 6 inches of lumber. Jigsaws are meant for fine detail work, not large straight cuts.

However, a close cousin is the reciprocating saw like the Bosch RS35. Larger motor, much heavier blades. You still have the problem of squaring off the bottom of the notch, but if you use a large auger bit to make a series of holes you will be able to remove the bulk with one good hammer hit and then use a thinner blade or a chisel to flatten out the bottom.

If you have a large number and want to mass-produce the notches I would rent a 12 to 16 inch circular saw, line up all the posts, bind them together, and make a jig to hold the saw in position on the ends. Cut, move blade down a bit, repeat.