Dan White wrote:

Also, would you cut out the tops of the 4/4 (if I go with those) to rest the
2/4 into as he did, or would you just brace and screw it together?

Just in case you haven't gotten, or read, some of the other responses, "4/4"
and "4x4" are two different animals. The first is pronounced "four quarter"
and refers to ordinary 1" stock, which is actually about 13/16". The second
is pronounced "four by four" and refers to dimensional lumber which is
actually 3 15/32" by 3 15/32".

And again, 4/4 is all you need.

--
It's turtles, all the way down