How to best add chassis ground to vintage integrated stereo?

Hi there, new here and not sure if this is appropriate spot to post this but maybe someone has redirection feedback or a link/reference-- many thanks.

I have an early 1970s Braun integrated stereo with turntable. Its entire casing is sheet metal, and the plug is only two-pin, ungrounded. I'm planning to recap the power supply and do some other servicing, and while I'm at it I'd like to add a safety-ground to the case... for safety 🙂

What's the right way of thinking about this while avoiding ground loops? Currently in the turntable section, the tonearm tube is "grounded" to the chassis, which in turn flows into the "ground" lines of the amp circuitry, but because everything is behind the power transformer, none of it actually goes out to the neutral line of the plug as far as I can tell.

I know enough to be dangerous here but fuzzy enough that I'm not especially conversant in how ground loops happen. Can anyone suggest how the "grounding" path is actually working now without a safety-ground connection (for my enlightenment)? And I know I can simply screw the safety ground into the chassis's metal case but I don't know if I'll need to think about anything else to avoid creating any other issues/loops?
 
It's an Audio 310, c. 1972. Manufactured/sold in Germany. I'm in the US. It's voltage switchable (I use it at 110) although it wants 50Hz for the turntable motor. (I have an aftermarket inboard frequency converter wired into just the motor line to get 60Hz to the motor; motor circuit doesn't run through the transformer/power supply section) It's been operating in this configuration for a decade or so, and I haven't made any other electrical alterations to it except putting a (polarized) US plug on the power cord.

Thanks
 
Wait and see if someone with Braun experience has advice.

If used in a home on wood or carpet floors, _I_ would leave it 2-prong cord. This is not a guitar amplifier which is carried around, played in beer-puddles, near PA microphones, and the user is *constantly* touching the amplifier (via guitar cord). And it is not a cheap unit.

While I am adamant that guitar amplifiers should be grounded, my feelings on home hi-fi are far more relaxed. True hot-chassis amps will give you a strong tingle, and sometimes not even that if the floor is insulating and you don't have PA mikes.

However bonding the metal(?) case to the wall 3rd-pin is unlikely to make a ground loop (you only have the one thing and one ground). This can be tested with a clip lead.
 
Thanks PRR. I guess I'd been assuming that best practice as a matter of course here would be adding a safety earth ground but it sounds as though that's just not necessarily best practice even with the metal chassis since it's been designed to go without. (Understood re: amps and beer puddles, I've been there.)
 
Yesterday I did the same thing on an 70's ADC Soundshaper MKII (Metal chassis & aluminum front). What I did was connecting a ground wire to the chassis and another wire to the PSU ground between the capacitors. It's working fine with my Pioneer grounded stereo.