While strictly Class C does have a host limit, altering the subnet mask and moving into classless addressing should work with the IPs/Mask that was given out by the SME DHCP server.
To accept your solution would imply that SME accepts erroneous information during set-up and from that produces an unworkable addressing assignment.
What type of switch are you using?
It's just a regular SMC 10/100 8-port (or more, can't remember off the top of my head) switch used in all the classrooms and other places.