Joining 2 fabrics sideways?

[gnothiseauton]

This is actually a repost, and I was hoping to get a few more ideas since I haven't been too successful so far.

I am having to piece parts of a shawl together. I am not following a pattern, and am fairly new to knitting. Both pieces are in St st with slip-st edges. They are both square, 108 st by 144 rows. I need to sew the side of one piece to the top of the other (as cleanly and seamlessly as possible of course).

I've figured out that I need to sew 3 top-facing K sts for every 4 sideways-facing rows to stay even. So with a slip-st edge (1 slip-st every 2 rows right?) I'm alternating sewing 2 top-facing K st into one side slip-st and then one top to one slip (*2 top/one side ; 1 top/one side* rep from *).

So then I'm stuck! How does one sew as seamlessly as possible side to top facing fabric? Neither kitchener nor matress st will work i don't think since they both require same-direction fabric.

HELP!!!!!!!!!!!!!!!