I used the stopwatch method for several years. I made up a little pocket sized card using an Excel spreadsheet as a cheat sheet. My DD used to have a pitching coach that had the SpeedTrac displays. He had them on the floor as you described, but they were ALL over the place on speed. I did much better with my stopwatch. It could have been the placement though - and these were older devices.
I bought a Bushnell gun a few years ago. I compared the Bushnell's readings to freeway speed readings on my GPS, and it was accurate to 1 mph. I think most of the inaccuracy problems you hear about these guns are caused by operator errors and misuse. The problem with the gun (at games) is you need to be "in-line" with the travel of the pitch. So you're going to be the geek standing behind the backstop trying to get a clear shot through the screen. With a stopwatch, you can sit anywhere that you can see the pitch release and the catcher's mitt.
I charted her speeds with the gun at practices, where you can stand BEHIND the pitcher out of harms way. I got the same readings as when standing behind the catcher. But after using the gun awhile, I surmised that it was good enough using the stopwatch - and a LOT more convenient.
Measuring pitch speed is not (and should not be) an exact science. Your goal should be more of a reference and general comparison than anything. You can tell with a cheap stopwatch if she's throwing 60 or over. You can also tell if she's only throwing in the low 50s.
Another overlooked method of measuring speed (which is VERY accurate AND foolproof) is to use a digital camcorder. You just step through the footage frame-by-frame, counting the frames from pitch release until the ball hits the catcher's mitt. At 30 frames per second, you can do the math. With the video, you may even see some mechanics issues to work on!