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

Update 3:

Match - takes one or more criteria-pattern pairs; User, Group, Host, LocalAddress, LocalPort, RDomain, and Address. Or the single token All which matches all criteria.

PrintLastLog - sshd(8) should print the date and time of the last user login

PrintMotd - Specifies whether sshd(8) should print /etc/motd when a user logs in interactively.

Non-standard SSH daemons like dropbear(8) may die with advance configurations like Match statements.

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