Battery-powered boost converter for neon glow lamp

I'm working on a battery-powered DC-DC boost converter for neon glow lamps. It's a switched-mode booster with a 9-volt battery providing input power. The output needs to be at least 90 volts or so, with a current draw in the range of 10 μA to 1 mA. For the target application I also need it to be very quiet below 1 MHz. These constraints (relatively high voltage, very low current, high frequency) puts it in an unusual corner of design-parameter space where I haven't found any ICs (integrated circuits) for sale.

So I'm rolling my own that will ultimately use a CMOS 555 timer (LMC or TLC) as a switch. I'm working my way up in frequency and am currently using a standard NE555. I've been breadboarding square-wave oscillators to compare the recommended datasheet configuration to some alternatives. The other night I felt lucky and skipped ahead and quickly implemented the rest of the booster using an available MPSA42 "high voltage" NPN BJT, a 4.7 mH axial inductor with unknown stray capacitance and self-resonance frequency and a neon glow lamp as the load. Here's the result:

Neon glow lamp DC-DC boost converter MkI. It's beautiful to me!

Close up with NE555 DIP-8 IC on the left and TO-92 MPSA42 BJT to its east-southeast. To the left of the glow lamp is an oversized black diode, with the green inductor behind it and the brown filter capacitor behind its anode lead.

And zoomed out: no cheating, the 9V battery is the only power source

So I passed the first milestone: I am powering a neon glow lamp with a 9V battery! The open-circuit output voltage was 120V. The good performance of the MPSA42 transistor was a positive surprise. It probably wasn't intended for power supplies, but I'll keep it at least for the next few design iterations. However, getting the operating frequency above a megahertz will require some effort. While I'm waiting for promising inductors to arrive (hopefully with low enough stray capacitance), I'm doing circuit simulations with ngspice, but that's another post.