Thanks for the quick responses.. I've seen the "two balls of yarn" solution elsewhere.. I think that's the best way to do it..
When you use one skein of yarn, and cut it and then cut it again to finish the far side of the vertical slit you are basically "creating" another skein of yarn...
So it's easier just to use another skein- although actually you can just pull off a few yards of yarn from your skein before you begin to to this... (If you're using one large skein)..
Or even use another color for a dramatic accent to the skein.
...I have a THEORY that you might be able, after you knit your first "half row" to maybe pull forward a huge loop of yarn, keep it to the side, keep knitting the near side of the slit..
...then somehow use this extra loop to finish the other side of the slit..
..and when you reach the "finisher" row of the slit, somehow join this loop back and then go back to knitting garter as usual.
The loop would have to be flexible somehow, so that you could just pull it through to tighten into place.. so that it wouldn't be visible other than maybe more than just an extra line of yarn..
...wish me luck on the big experiment!!!