You're right that many of these CTV's don't like variac's or limiters and you're forced down the "just power it on" route.
This is where preparatory checks are crucial and I normally spend a great deal of time beforehand, sometimes a day or so inspecting the boards and components looking for problems. For example on the recently repaired Aphelion
I went over the entire circuit removing every module checking all the electrolytics with an E-S-R meter and replacing where necessary. Also when coming across obviously failed caps or resistors or diodes doing the same. Only then powering up.
Having worked on quite a few Thorn 3000's/3500's which equally hate variac's, my approach is to always get the power supply module on the bench and get that functioning first, nothing else is tackled until that's on spec. Once the PSU is working its placed in the set then and only then, is the whole set introduced to power.Now I'm NOT suggesting you remove every module from your set on your first CTV repair
as therein you're likely to invite trouble but, with some of the above in mind if it were me in your position, I would remove the power supply module from the A823. Then spend some time getting familiar with it, inspecting all
the components in the supply rails so that you're happy they are OK. I might even suggest removing the 2x 600uF's putting them on the reformer so as to gently introduce them to power. If they reformed great, if not, then replace them. However If you don't have a reformer ( do you?) and are reasonably happy the power supply checks out OK, like Neil I would introduce it to power but with the tripler disconnected ready to quickly turn off at the first sign of trouble.
Assuming no drama after 5 mins or so, I would switch off and feel the big 2x 600uF ( be very careful when doing so not to contact the terminals) can's for over-heating. Do they seem cool? If so power on again and leave longer repeating the process until confident they were reforming or have reformed themselves. If not and at any point they start to feel HOT, replace. Once past that stage I would then connect the tripler by this time the set will have already informed you of its initial state and you will have been checking rails with your meter, you will also have noted sound or no sound. Now with the tripler reconnected raster, no raster. I/F working? Input a signal snow or no snow, tune in a colour bar or test card F, colour or no colour? If the latter disable the colour killer to see what the decoder is telling you.
You may be lucky with the set rewarding you with a good account ( you may find that a bore and want some fault finding fun) but be aware that any stage, expect the unexpected. With these all solid state sets longer use and elderly components especially those three legged beasties, inevitably start to baulk at being woken up. You may as I have found take many steps backwards from the initial state which can be frustrating, it will test your confidence and resolve to see it through.
Just my two-penneth, others may agree or disagree with the approach, either way I hope it helped.
p.s sorry to have waffled on and apologies for any unintentional egg sucking.Edit1 :
Cross posted with Andrew ( I should type quicker) looks like we sing from a similar sheet.Edit 2:
Oh and find the filter cap across the mains and remove/replace it. Only if you're like me and hate loud bangs, if not ignore and enjoy the ride