Not sure about (New) Piper but Bombardier, Cessna, Gulfstream & Raytheon (Beech) all have Brits in their employ to my knowledge. Don't forget that Raytheon took over the HS125 and brought almost the entire Chester design team to Wichita to build it - so much so that Airbus had to open a Design Office there to do the 380 wing (Chester did the original 'bus wings).
The main problem could be getting a visa - talked to a Gulfstream engineer last week (a fellow Brit) and he said they'd hit the limit with no new Green Cards available in their region until 2007. Not aware of any such restrictions in Canada for engineers rather than pilots (see the Canada forum for never-ending threads on that).
"The British aircraft industry is alive & well and living in Wichita, Kansas"