Adding chassis earth to vintage receiver

Hello all,
I'm reburbishing an early '60s Fisher 500C receiver, (7591 output in push pull pairs). As on most units of the era in the US, there was a reversible two prong plug hard wired into the unit. The input power wires are grounded through a 0.01uF cap paralleled by an 820K resistor.

http://oldtech.net/Fisher/500C/Schem.pdf

I'd love to install a modern IEC three prong with integral fuse for safety, and connect the chassis to the earth lead. I'm concerned that this might negatively affect the sound, though, as the signal earth is the chassis, and there are dozens of soldered connections all over the chassis, so there is no easy way to raise the signal earth off the chassis.

Has anyone done this with an older unit? Any thoughts on safety vs. sound?
Thanks,
Mark