Wow that baretter is HUGE.

I have one with a similar shape, but nowhere as big.

See https://vintage-radio.com.au/home.asp?f=2&th=688&offset=2#6539 for photos.

There are two STC Model 633 sets listed on Page 330 of the 1939 Radio Trade Annual & Service Manual both AC radios.

633H - Valves 6U7G, 6K8G, 6U7G, 6Q7G, 6AG6G, 5Z4G

633K - Valves 6U7G, 6K8G, 6U7G, 6Q7G, 6AG6G, 5Z4G

The 633H is listed under Cabinet as 'Con' and had a 'Tuning Indicator'.

The 633K is listed under Cabinet as 'Comb' and did not have a 'Tuning Indicator'.

In the same publication there are sets by other manufacturers that are shown as 'Universal' under Power Source and includes the note 'Incorporates type 302 Barretter as a filament voltage regulator'. Other sets had a Type C1 Barretter.

If you don't want to mess up the chassis? That is a console and there is plenty of room in there. Given a suitable transformer (which you seem to have) It can be mounted in a grounded metal box on the floor of the cabinet. One of the things I do is ensure that the radio connects via a plug. This can be a recycled valve base, which, with a drill; Some heavy non conductive card like "Elephant hide" a zip tie copper wire can be made safely.

That enables it to be a power supply for other sets. The normal ground /shield for an octal socket is Pin1; Heaters 2 & 7 ; Beware of back bias (B-) does not always go directly to chassis. The chassis can be grounded where there is a transformer (not auto transformer) between set and the mains. Barretter can then be kept as a decoration.

Stagger the heater pins rather than connect all say pin 2's and pins 7 in parallel. E.g. start say 2active & 7neutral then next 7active & 2 Neutral.

Here is a site that shows the patterns of various Magic Eyes.

http://www.magiceyetubes.com/patterns.htm

Regards

Wayne.