There are two fundamental parameters about analogue meter movements that need to be considered.
One is the resistance it presents to the circuit in which it is placed and how that circuit performs. The other is the current it can handle. Exceeding the FSD current is not advised, since you can mechanically damage the movement as well as cause overheating of the coil.
With those things considered, this design calls for a 100uA meter movement - so it can be reasonably expected that currents up to this figure can be present. By putting your 80's meter in there on the 50uA range, you risk overdriving it.
Typical of meters back in those days, the sensitivity of meters was expressed in ohms per volt - with 20,000 ohms per volt (DC) being considered the minimum acceptable for electronics work. This sensitivity figure should be found on the meter's scale - something like this:
If your meter
is 20,000 ohms per volt (DC), then when you work out the math - you get 50uA sensitivity. This is the sensitivity of the meter movement alone - where there is
no shunt and all the current you are measuring goes through the coil.
Of course, you can set the meter at the next highest scale and you will be safe. If that is a 250uA scale, then you'll only get a maximum of 40% deflection - but that could be adequate for your needs. Unfortunately, a lot of meters jump up to a 2.5mA range or thereabouts - which is 25 times your 100uA requirement. The setup would work, but your needle would only move over 4% of the meter's full scale deflection.
The solution is to add your own shunt resistor. To double the 50uA range, this resistor would need to be the same value as the resistance the meter presents on this range. But don't simply go grabbing another meter to do a resistance check! If the current put out by the measuring meter goes above the limit of the meter movement, you could damage it.
The simplest way I could suggest to get the coil resistance safely is to first open the back and locate the actual connection points on the back of the meter movement itself. You will need to measure the voltage on these two points. Then, set the meter to a resistance range, short the leads together and adjust for zero ohms. Here, the meter movement is at FSD. Measure the voltage across the meter movement - but use a modern DMM. These typically have 10M (or higher) input impedance which is what you want, so that you don't disturb the voltage you are measuring by any amount worth worrying about.
Take that voltage and the 50uA and plug these into Ohms Law. This will give you the value of the coil resistance - and you can work out your own shunts from there.
If you wanted to do this for a calibrated scale, then you will need to get very precise values for your shunt resistors - but if you are going for a dip oscillator, you're not really going to be too interested in high accuracy, just finding a minimum point.
In my personal opinion, this sort of application is where analogue meter movements have a distinct advantage over digital.