What is the proper email etiquette when contacting potential supervisors on short notice?
The first few tips is be cordial and be brief and to the point.

Make sure you use the correct title and spell the name correctly, in fact make sure the entire mail is spell checked and grammatically correct, anything else sends a bad signal.

Begin by stating your purpose for the mail and provide a short but detailed reason for why you approach the person in question. In your case you should also explain the "short notice" and excuse yourself very concisely for the inconvenience this could bring on. 

Follow up by providing a brief statement of why you are interested in the subject but also the school and/or research group. Continue by describing your background and how you see your background being an asset in working in the PhD field.

All this should not be more than 2-3 paragraphs of maybe 5-10 sentences. A short e-mail which manages to say the essentials will be more likely to succeed than a long and very long-winded detailed account (that no-one would take the time to read).

The tone of the mail should be respectful but do not excuse yourself or play "underdog", be confident, brief and to the point. that will impress more.

Finally attach a CV and provide any MS thesis papers you may have.