Although I haven't set check_spool_space, Exim is still checking the amount of space on the spool for incoming SMTP messages that use the SIZE option. Can I suppress this?

The RFC for the SIZE option says: *If the server currently lacks sufficient resources to accept a message of the indicated size, but may be able to accept the message at a later time, it responds with code

452 insufficient system storage

and that is what Exim is trying to implement. This is entirely independent from check_spool_space, which says don't accept any mail if there is less than so much space in the spool partition, though the code is optimised to do both checks at the same time if required. However, you can suppress the SIZE check if you want to, by unsetting smtp_check_spool_space.