Thank you very much, Pete, for the insights! It will be great to have someone that's done this before as a resource. I have a few questions.
First, I did think about driving the FET from 3.3V, so I selected it carefully. I am using the Vishay TN2404K, and assuming a Vgs of 3.3V, it looks like Rds(on) is about 2.3 ohms:

Assuming 35mA max current draw (ballparking 4 IN-18 tubes as worst case), the voltage drop across the FET would be about 81mV, and the power dissipation about 3mW. The datasheet says the FET is capable of 360mW of dissipation (at room temp), so I felt pretty good about using them. Is there something I am missing there?
(As a cheaper alternative I may use the BSS131, which I am already using to drive the nixie channels. Making the same assumptions, Rds(on) is about 10.3 ohms, which a voltage drop of 361 mV, and power dissipation of about 13mW, still well below the limit.)
Second, I was planning on running the PWM at 200kHz because it allows the boost to run in continuous mode with a much smaller load. This way I can test with a single nixie (around 1.5mA). I have worked through the boost calculations and the PWM register values in a spreadsheet
here. Please take a look if you are curious. I may be off base with my desired values.
One concern I had based on your feedback is the ratio of the A to B register. This ratio sets the duty cycle of the PWM output, right? To boost 24V to 200V, I need to duty cycle of 88%, which exceeds your recommendation of 80% max. Can you talk a little bit about why this is important? I know the inductor needs some time to discharge, but isn't controlling that on/off time the only way to set the output voltage?
I also had a question about driving the FET gate. Why set the pin to an input and rely on the pulldown rather than driving the pin low?
I really like the soft start idea and the guidance about using the ADC interrupt routine. Plus I appreciate your advice on ramping the voltage up slowly, I will make sure I take care when testing (and especially debugging). Good to know about the HV5530 at 5V too!
-Brian