Gmail – Force Gmail to always pop out the compose window

In short: not really. You could, however, stick your PDF resumé online somewhere (say in a Dropbox public folder) and link to it in your signature, which will get past corporate attachment filters.

However, I would recommend that you link to your LinkedIn profile, in your signature. If you don't have one, create one today. Like the service or not, it's a widely-used tool for recruiters and jobseekers. You can upload your existing resumé and get past 90% of the fiddly data entry in one shot.

Some friendly and off-topic advice: don't use a canned cover letter. The purpose of a cover letter is to address and to respond to the specific requirements of the job to which you're applying. You don't sell yourself to a manager by making yourself sound great in abstraction: you sell yourself by making yourself sound appealing to the person who needs to fill a specific position and who is looking for specific qualities and skills related to that position.

A very common mistake made by jobseekers is to look at the job hunt from their perspective, "I need a job," rather than from the hiring manager's perspective, "I have a problem I need solved." Rarely will HR's motivation be "I have money I need to spend so let's hire someone." (/advice topic="off" ;)

I like tinkering with Gmail, so I made a small script to do what you asked. It works for me in Firefox 5.0 with Greasemonkey.

The shortcut is Ctrl+Shift+Z. You can go through the source and change the shortcut if you wish.