> wood stove ... put inside the dog to dry him seemed excessive to me
I know you are joking.
You know how bad burned dog-hair smells.
But I realized sunny Italy may not have the type of clothes dryer which is common in the US. For one, ours uses 4,500 Watts, and we know your homes are not wired to supply that much for very long. However the dryers can also be made to use gas fuel, and must be common in laundromats (commercial clothes-washing establishments, sometimes coin-operated).
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> inject the trem at the V1 grid and needed signal size would only be a couple-hundred millivolts
Here we must consider the dog-to-dryer ratio.
A 3-pound Chihuahua in a 30-pound dryer drum will hardly wobble at all. Put in the Corgi, it is rock-and-roll.
Likewise to get any good variation of gain, we must drive the tube HARD. Say the tube runs Normal with 1mA. We want at least a 0.5mA-1.5mA variation of current to get a 5dB variation of gain. To get "deep trem" we may have to push to 0.1mA-2mA. Essentially "zero" to "double".
This means the peak trem grid voltage will be "similar" to the bias voltage.
Many guitar first-preamp stages run 1V bias. A "couple-hundred millivolts" is a start but may not be satisfying.
Note that with 1V trem and 0.1V guitar, the 10Hz wobble at the plate is likely to be ten times bigger than the guitar signal. The stage after may pass guitar fine but be overloaded by 10Hz. Most of the low-level tricks "need" a several-stage C-R low-cut filter after the tremolated stage.
IMHO, Push-Pull is THE answer. You run the signal out-of-phase, the trem in-phase, and wire the output to reject in-phase variations. Conveniently this will usually be your HIGH-level stage (6V6 etc) so the trem/signal ratio is not so big.
If you can still get them, photo-resistors are a natural. They are tricky to set up, and I don't think they have the "soul" of beating big bottles push-pull, but can be used with any type amplifier. Sadly they are going extinct.
VCAs (controlled gain amplifiers) are what we really want (after cheapness, simplicity, sound, and elegance). The old '3080 wasn't too good and is also going extinct (more fakes than reals on the market). THAT Corp has excellent VCAs, but cost more than a buck, and mucho-mucho mas by the time you house, interface, and feed them inside a tube amp.
To state the obvious-- the Usual Culprits sell $49 trem pedals at the nearest banjo shop, $29 on Saturday Sale.