How can I effectively "sentry jump" with the wrangler?

You can reduce damage and fly farther by jumping and crouching in mid-air as you shoot the rocket.

To answer your other question, I present you a page of helpful videos instead.

I'm honestly not sure about using the gun to propel, or if you can microsecond-time the pickup of the sentry post rocketblast. However, the fairly obvious tip would be to build a teleporter exit in a safe spot wherever you rocket jump to and have your entrance waiting in a convenient spot for afterwards. You'll be able to move your sentry / dispenser quickly without the hassle of having to rebuild everything.