Finally got some time to pay attention to this task.
I ordered two diameters of tubing -- 1/8" and 5/32". The 1/8" slips too easily through the slot in the edge of the awning cover slat, so I elected to use the 5/32", which will barely fit down the sewn tube in the edge of the fabric.
In order to get the nylon tube to fit at all, you have to clean out the edge of the fabric. A straightened out clothes hangar is long enough to reach the length of each of the individual fabric stips (the entire fabric is made from narrow pieces, about 30" wide). I put a small hook on the end of the hangar wire to catch the remants of the old fiber cord in the sewn tube. You have to run the wire through the fabric several times to get everything.
1. Snip the fabric about 1/2" from each major seam. The allows you to slip the wire in one end and all the way through and out the other.
2. Run the hook through the edge several times, until you stop pulling out small pieces of brownish fuzz that looks like old wool.
3. Cut the end of the nylon tube on a 45 degree angle and push it in through the snip. If you can't get the tube through at least half the width, then pull it back out and see if it's got brown fuzz stuffed in it. If so, run the wire through again. I've been unable to get the nylong tube to go the full width, so I insert another length in from the other snip.
4. When the first tube is in as far as I can push it, a little more than half way, I cut it off and then grab it through the fabric and pull it back so that the tube slides into the 1/2" of edge that's towards the seam. I'm thinking that having some tube inside that snip (cut) will help when I'm trying to insert the fabric back into the aluminum roller cover.
5. Insert the tube from the other end, until it meets with the piece that was previously inserted. Then cut it and work it back into the 1/2" piece of the edge. This will leave a small length of edge without any tube in it, right in the middle of the section. You'll also have a gap in the seam area.
Now, the next trick will be to order a new slat from Zip-Dee. If it's longer than 8', it has to be shipped by freight, which costs over $100, more than the slat. So for my 20'-7" roller, I'm going to order 3 slats that are 7' long and cut one of them so that they make a single long slat that is the exact length. I don't think having two slits in the slat will be a problem. The fabric will still be covered from UV and it doesn't mind gettng wet (it's nylon).