Jeff:  I had the same GPS dropping out problem differently:  I had both the Chelton antenna and a Garmin 530 antenna mounted in front of the panel under the glare shield in a fashion similar to what you describe (standard Lancair Avionics position of about 5 years ago, they have since changed to a different configuration I am told).  The Chelton remained solid but the 530 lost GPS shortly after takeoff during climb and regained a solid signal during descent for landing.  Since it has a satellite page I could monitor the signal as it deteriorated uniformly.  No such page is available on the Chelton so I cannot comment regards its signal strength but it very seldom experienced GPS dropout.  I replaced the antenna, cable and just about everything but the actual box because I could not believe the location was the problem since I had an antenna mounted 18" to the left of it that worked fine--no joy.  I also tried RG-400, RG-58 a spec 17 dB signal attenuater from Coment and none of that helped (anyone want to buy a $125 signal attenuater?).   I was ready to send the box in for a WAAS upgrade just so I could get the GPS receiver looked at when I decided to chuck logic and move the antenna to the tail for a try.  Well of course the problem was solved!   

good luck!

paul (LIV N94PT just coming out of paint)