I selected a bleached linen for the shade, which is an off-white.   I doesn't color the light very much, so it's a fairly white light in the end.  Here I'm testing the fabric laid over the pvc lampshde liner with the LED light assembly underneath.  There's no blue tinge, which is good, but I think I'd prefer a slightly warmer white for a mid century modern lamp.   I may end up buying another spool of LED strip with a warmer temp.  I'll set with it for a while, though.

The pvc sheet is cut to the desired shape, leaving about 3/4" extra on one of the straight edges for an overlap.  The pvc has adhesive on one side, and it gets adhered to the fabric.

The fabric is trimmed afterwards, leaving a border on 3 sides.

The top and bottom border gets wrapped around the metal hoops that define the top and bottom circumferences.  The hoops I used were not intended to be used for lampshades, and were smaller diameter wire than what's normally used.   This did make it a little less forgiving to wrap.   The rings are first wrapped in a double-sided tape.  The border gets wrapped around it and tucked next to the pvc on the inside.   This is a trial with some scrap fabric and pvc just to get the hang of it.

Rolling the two rings along the pvc edges simultaneously, by yourself, is tricky.  (I was too impatient to wait for my wife to help me.)  I didn't get any photos of that stressful part.  This was the end result. 

The overlapping long seam wanted to bulge, so I left the film on the sticky tape until the cone shape fully formed around the hoops.   On the interior (not shown), I put some blue tape over the interior of the seam to hold it together temporarily.  Then, I started pulling back the seam tape film a little at a time as I smoothed the seam down on the interior.

The fabric border is then folded carefully around the hoop, ideally with no wrinkles.  I ended up having some unevenness on the edge when I was finished.  I'm sure I'd do better on my next lampshade.

Then the excess fabric is tucked all around the hoop behind the pvc liner.  I found that a credit card worked well for this.  With all the fabric and loose strands tucked-in, the shade was complete.