Yes, I have the same problem. GL songs seem to demand a GL voice. Luckily, my voice has roughly the same range as Gord's (not as pretty as his, of course, but what can you do), and it's like second nature to drop into that deep, booming timber whenever singing one of his songs. Fitzgerald wouldn't be the same without that timber, and many other songs would be so much less recognizable. It's almost a requirement to "impersonate" Gord on these songs, and I do so with the utmost respect (even if I don't always quite hit the mark...).
Dan