Yes your likely problem is the transformer turns ratio. I’d guess this is an 8 ohm output transformer with an about 80 ohm secondary from the voltage you are seeing. For 5V in and 50v out you have about a 10/1 turn ratio (which translates approximately to the impedance ratio of 8 ohms to 80 ohms). The transformer you need wants a 80/1 or so ratio to increase 5V to 400V. I think the value of the capacitor (and possibly the impedance of the transformer) will control the oscillation frequency of this (it is quite a clever simple oscillator circuit I must admit!). Note that you need 1kv of isolation which tends to be expensive (a 100V isolation is in the $2/$3 range for 600ohm/8ohm, 1KV isolation is $14 or more). What might work best is a 220volt to 6V power transformer. If you feed the 6V side with 12V the line side should produce 440V. I’m not sure this oscillator circuit will work (it would need to be in the 50/60hz range to work correctly) but a 555 oscillator at 60hz driving a MOSFET in place of the transistor should work. Note you want to be careful around the 400V output, with the cap that is getting to be enough energy to kill you if you touch it.
edit: One of these may do as well, somewhat pricey and shipping may be an issue
Peter