Thanks for the tip. I was able to set uc_cart_checkout_form to multipart/form-data using hook_form_alter. However, this didn't seem to solve the problem.

I should mention that there are actually two forms on the site: uc_cart_checkout_form and resource_node_form. resource_node_form is contained within uc_cart_checkout_form. Both are now set to multipart.

I'd really appreciate any other advice you can offer.