Dixiecat, I'm not sure that it would have been cut from the same bolt, but I do remember something about a double width run of the fabric. It's asymmetrical, so everything on the other side of the middle line might have been reversed on the warp. I think that might change the twill lines etc. It's hard enough to understand it just from the thread count; that's all I have to go by on tartan.
I'm in garment sewing mode here so bare with me a moment. Let me see if I can convey what's rolling around in my head to my keyboard.

Let's assume these facts:
1) tartan is asymmetrical
2) kilt is made from double width fabric that has been split and rotated as per Appendix E of The Book
3) an extra yard of fabric was ordered and cut from the same bolt

if 3) was cut from a single width of this fabric (1 yd by 30" approx) then yes, you will have trouble with twill lines, and when rotated to match twill lines, you won't be able to match the asymmetric lines unless you were given a piece from the same half of the double width as was used for the kilt.

but, if 3) was cut from a double width (1 yd by 60" approx), it will match. It should be just a matter of moving the fabric around to the proper half double width that was used for the kilt.

If we change the facts to:
1) tartan is asymmetrical
2) kilt is made from an 8yd length of double width tartan fabric that has NOT been joined. This means that the double width was split down the middle and TWO kilts are made. One kilt would be made with the wrong side out to keep the twill lines in the right direction.
3) an extra yard of fabric was ordered and cut from the same bolt

if 3) was cut from a single width of this fabric (1 yd by 30" approx) and is from the same half of double width that was used for the kilt, it will match

if 3) was cut from a single width of this fabric (1 yd by 30" approx) and is NOT from the same half of double width that was used for the kilt, it will NOT match

but, if 3) was cut from a double width (1 yd by 60" approx), it will match as you'll have both sides of the middle. It should be just a matter of moving the fabric around to the proper half of the double width that was used for the kilt.

I apologise for beating this horse, but I'm having trouble in seeing past the assumptions that I've made above (ya, ya, I'm gettin' old). Please point out where my thinking is in err. Pictures and hand puppets could help.

Now, assuming that you have a matching piece, you have duplicate your front pattern piece to have a left and right layout and then layout the pattern piece for the waistcoat right sides up using the same stripe as your center front for both pieces and should be the same stripe as the center front of your apron. This is the only way to get your asymmetrical tartan to follow the sett across the front of the waistcoat.