Can I disable SSH last-login and MOTD on a per-user basis?

Yes you can, add the Match User directive to your sshd_config file like so:

Match User root 
    PrintlastLog no
    PrintMotd no

The Match directive also works for Group and Address to match for GEOS/Unix group and IP Address retrospectively.

Update:

As a per user basis without access to the sshd_config then you would just create an empty file in $HOME/.hushlogin which would prevent bash in interactive mode to output these alerts. This also works under other systems that use login(1) such as telnet and screen sessions.

Update 2:

To surpress the Banner output from sshd on a per session basis use ssh -q <host>or include LogLevel quiet in your ~/.ssh/config

Not all OpenSSH implementations as those in Ubuntu allow PrintMotd or PrintlastLog in Match User section.

One may find this askubuntu question usefull with some workaround if s/he got error like:

/etc/ssh/sshd_config line 97: Directive 'PrintMotd' is not allowed within a Match block