Here's what I've read...

You should use a fingernail to try to puncture the skin. If you can do this / if the indention made by your fingernail fills with moisture, it's not mature and won't last in storage.

Cushaws are planted in May or June and mature in 90 to 110 days. Mature/ripe cushaws should last about 4 months in cool storage.

I haven't grown this variety, but I just purchased some cushaws yesterday at the Amish market, and they were ivory and green striped, not tan at all. They assured me they were terrific for eating, but like other winter squashes were also great long term keepers. If yours are tan colored I wonder is they are too mature?

I hope this helps.

http://www.slowfoodusa.org/index.php/programs/ark_product_detail/green_striped_cushaw/

http://www.localharvest.org/ark-product.jsp?id=108