[Arran]

Let's have a look in the 1937 Sylvania tube manual that I have. The 6E7 is a variable Mu, RF pentode, so that would be used for both the IF and the RF tubes. According to this book electrically it's the same as a 6D6, but it has a 7 pin base rather then a six pin one, pin 5 on the 6E6 is not used. The next tube, the 6A7S is just a 6A7 with a metal spray coating, a Goat shield is a viable go around unless you want to experiment with metallic paints on glass. The 6C7 is a dual diode, triode, so likely performing the first audio, detector, and AVC functions, again the buggers used a seven pin base as opposed to a six pin, nothing is connected to pin 3, but electrically I can't find an exact sub at this time, but a 6R7 or 6R7G looks to be the closest, which are octal based. As for the 6Y5 it looks like an 84 (or a 6X5) would be the closest electrically, actually an improvement since it can deliver more DC output current, and uses a 500 ma heater rather then an 800 ma heater, but the 84 uses a 5 pin base rather then a 6 pin one, but pin 2 on the 6Y5 is unused anyhow. In three cases you would either need to change the socket, or build an adapter (if there is room for one).
Unlike with Rogers in Canada, Grigsby Grunow went belly up in 1934, and the replacements stopped being made at least a decade earlier then the Rogers ones, so the tubes may have been pinched from the car radio a long time ago. Rogers also had the good sense to make mostly standard tubes with spray shields, and even boasted that you could sub them for the new RCA metal tubes when they came out, on their octal types they followed the number with the letter "M" for metal spray, as opposed to "G" for the standard glass octal types, or "S" on the older based spray shield tubes. Sometimes they would invent their own number like a "41M" but it was really just a 6K6G with a metal spray coating, which a power amplifier tube does not need. There were four weird ones they started making during the mid to late 1930s, one was the 2X3 (half of a 5Y3 in pinout), a 2Y3 which I have never seen (something akin to half a 5U4) a 6X6 which was magic eye, and a tube called a 6F7M (a 6F7 pentode triode with an octal base).
Regards
Arran