I would start by going back a step and removing the WiFi module - this appears to be a problem with the main board and not the WiFi module, so let's concentrate on that for the moment. I don't know of any way that the WiFi module could cause this, so let's eliminate that for a second.
So please take out the ESP for the moment and then try the startup test again.
I can think of a couple of things that could cause failed startups - but they don't match with the fact that the HV is there, as previously mentioned by Ty:
The RST pullup (R30) is faulty
The crystal or load caps (C5, C6) are borderline
The decoupling caps around the controller are borderline (C7, C8)
You can try fiddlling around with these, but I don't think that this can be the problem if the 170V is there. Please check this fact again, it is key to the fault finding! If the HV is there when the startup fails, we can exclude the clock or reset circuit.
If you have a scope, we need to probe pin 1 of the opto-isolators. If you get a rectangle wave there (duty cycle 1:5) it has to be the K155, or the drive to it.
Thanks for posting good quality pictures. You'd be surprised at some of the grainy pixellated stuff we get posted here. Your soldering looks really good except for the one spot Ian already noted.
I have 2 recommendations that probably won't fix anything but are "best practices" stuff: Trim the leads on the 7805 since they are just begging to short on something. And scrub the solder side with flux remover and a toothbrush, or, if real flux remover is not readily available isopropyl alcohol is an adequate substitute. I've had enough "incidents" caused by stuff sticking to flux residue to make me pretty militant about board cleaning.
Ian, why do you suppose his HV is now reading 230 - 240 volts? Is it just because only 1 tube is lit? But if so wouldn't the slow HV control loop correct it downward? This should be telling us something, but what?
The RF shielding of the crystal is an interesting thing that hadn't occurred to me.
I have no further idea now but my concentration is being divided at the moment between this forum and some mods I'm making to a system that puts ketchup in cans (yeah, cans) for distribution to McDonalds restaurant kitchens. I'll be done with that for the day shortly and will give this problem a deeper look...
EDIT: I wouldn't mind at all if that clock were raised up on some screws or stand-offs or something. Just to get the solder side clear of the table top. Once again this is something that probably won't fix it but certainly can't hurt.
Look into it later when the dust is clearing off the crater.