How to measure EMI without special equipment?
Look at "SDR dongles" - USB dongles made ostensibly for laptop reception of TV broadcasts, but repurposed for amateur radio purposes and sold for tens of dollars. 

Not all of them cover the spectrum up to GPS frequencies but some do, so shop around.

Combine "SDR dongle" with "spectrum analyser" and "open source" search terms and I think you'll quickly have an outline of a solution - not a precision tool but something capable of diagnosing EMC problems and, if necessary, pre-qualifying equipment before expensive compliance testing.

Without doing any research I would suggest it's at least five orders of magnitude more sensitive (detecting microvolt signals) than your schematic of a diode-based wavemeter (detecting 0.x volt signals), so it should show most local interference even if it can't display a GPS carrier as a peak on the spectrum analyser.

A couple of minutes on Google suggest that they ARE sensitive enough to detect GPS signals presumably through the usual GPS techniques for extracting information from the noise floor. This doesn't prove much in itself but gives me some confidence that this is a viable approach.

If anyone has more specific and detailed recommendations, please add a better answer (if it isn't too close to a shopping Q&amp;A).