The following approach worked for me in a similar situation.
At one point, I had over 10,000 comic books. It was really just a mountain of boxes. I derived no pleasure from having them all.
I made the decision that it was time to downsize. I started with a single box and began going through the comic books, one by one. With each book, I asked myself a rather simple question:
If I never see this book again, will I really care?
If the answer was yes, I held it off to the side.
If the answer was no, I put it one of two piles:
- Sell individually
- Sell as part of a lot
Fast forward three years, and roughly 85% of the books have sold. I made a little money and cleared out a whole lot of space.
The best part?
I still have every single thing that I really like. The collection went from 10,000 plus books down to less than 300.
I realize this doesn't help you with the logistics of selling your cards. However, it may help you when starting to whittle down your collection.