Back in the '80s, many consumer products with VFDs used single transistor blocking oscillators (similar to a 'Joule Thief'), with a small transformer with secondaries for the filament supply and to provide the HT for the VFD driver. Its difficult to stabilise the output of such a blocking oscillator circuit, so run it from a regulated supply and use a shunt regulator for the VFD HT supply, so the load on the transformer remains constant no matter how many segments are lit.
Its possible to do without a filament supply centre tap by using a resistive divider across the filament. Two resistors of five times the 'hot' resistance of the filament is a good place to start. Connect a Zener from the divider or secondary centre tap to ground to provide cathode bias to get sufficient negative Vgk to get full cutoff even at the negative peak of the filament end drive waveforms. If the required bias turns out to be close to 5V, you can also simply return the centre tap to your 5V rail, if it can handle the max current with all segments on without rising (guaranteed if the HT supply inverter is powered from the 5V rail).