Chris, I can't help you with the shades, but I wonder can you maybe change the harp size? I just purchased two swing arm lamps on CL a few months ago and hated the cheap shades but wound up finding some neat ones at a thrift store that happened to fit as if they were made special for them. The harp on mine is different than table lamp harps (it's called a cup harp) but I found some online at the link below. Hopefully this could save you from purchasing new shades which are way more costly than harps.
You might check locally for a lighting repair shop where you can try out the shades with various sizes of harps.

Here is a link that might be useful: lamp harps

I'll give that a try - thank you!

fenchels.com.

Excellent service, good price.
Dee

Good luck Chris!

Dee, that's nice to know since I don't live in the city anymore it will be easier to order online than drive the distance to get something in person.