Depending on what SSH is needed for, you may be able to achieve this goal (for non-trivial) files by using IPTables to terminate sessions if the packet size is bigger then, say 1400 bytes. This means that interactive ssh will mostly work, but as soon as something tries to send a 1500 byte packet - like scp should for a file larger then 1499 bytes assuming a standard MTU of 1500, it will terminate the connection.
This will also prevent the "catting" attack you mention.
Unfortunately this means that you may have problems editing some files with a text editor, if the screen needs to draw more then 1400 characters, or if you need to cat a long file or do a long directory listing.
In the simplest case a command to do this might look something like
iptables -I OUTPUT -p tcp --dport 22 -m length --length 1400 -j DROP
We can make this work better by combining the packet length checks with ipt_recent, so that you allow a limited number of packets larger then 1400 bytes within a set timeframe (say 8 packets per 5 seconds)- this would allow packets up to 12k to slip through, but may give you the interactivity you will need for editing files etc. You can, ofcourse tweek the number of packets.
This might look something like
iptables -I OUTPUT -p tcp --dport 22 -m length --length 1400 -m recent --name noscp --set
iptables -I OUTPUT -m recent --name noscp --update --seconds 5 --hitcount 8 -j DROP
A cluefull hacker can work around these limitations by setting an MTU of less then 1400 on his machine (or force mtu or similar). Also, while you can't limit this to certain users, you can limit it by IP by modifying the iptables lines as appropriate !!