1. Good on the RIFA. The last thing you need is for one of those things exploding. It’s a mess and it reallly stinks. Like a skunk.
2. You do not need a scope. Your DMM on AC volts gives you everything you need to know about ripple. The frequency is a don’t care, you couldn’t change if you had to. Well, not exactly true since it should 2x mains due to the full wave arrangement, it would be 1x if a diode was open but then it would have really, really bad ripple!
3. You can certainly try the TIP, it will at least confirm if it’s the problem. You can just bodge it in for a trial, don’t waste time making it pretty just test to see if the voltage comes up. Turn it with your meter connected to the -12.4 to measure it without wasting time, don’t leave it on any longer than necessary to let the voltage stabilize the measurement and turn it off. That way you limit any heating that should be minimal. If that brought the voltage up, great, then you do it right and heat sink it. If nothing changes, put the old part back. All that said, in that application, you should be able to tell if the device is bad by examining the three terminal voltages while in circuit when it’s on, it’s just a basic emitter follower/pass regulator.
4. There is no harm in going with 1000uf, 100v if it fits. The 470uf would certainly work since electrolytic tolerances can be wide, i.e. +80/-20%. To make it fit, you’ve also have the common values of 560 and 680uf. What ever works for you, it’s not critical so long as you meet the old minimum.
Not to be critical but you’ll learn that the “shotgun” repair methodology, that is just pulling and exchanging components because you don’t know how to troubleshoot and/or you cannot find anything obviously defective - is a recipe for failure. The more you do, the higher the probability you will damage a trace, pull a plate-thru or install a component incorrectly.
You need to spend some time to understand how the circuit works in order to troubleshoot. The HP service manuals always have a description of how things work and this supply is no exception. Section 4-35.
Couple that with the a basic understanding of the passive and active devices and you have a starting point to analyze the collection of parts in front of you and look for the voltage that isn’t what it should be. That’s where you start. If you pull a part and it checks okay, put it back it and make sure things still behave the same way as before. Don’t go changing six parts at once and then wonder why it still doesn’t work. Troubleshooting is an investigation where you apply your knowledge of what should be until you find something that is not as it should be and then determining why it’s wrong. Just throwing parts a problem is like being a blind squirrel. Yeah, once in awhile they find a nut but it’s just luck, not skill.
Some closing thoughts:
1) If you think a scope would expand your knowledge, one of those $20 eBay STM32 2.4 inch LCD things is all you need to troubleshoot a linear power supply. See the videos below.
2) I have a functional 6236B on my bench, if you want some voltages from a functional unit, ask away.
3) You might find this series of videos helpful, its a fair amount of content in the six episode playlist with the last episode using the information presented in the first five to explain some good troubleshooting ideas for linear supplies.
https://m.youtube.com/watch?v=9iPHTWFDXn0&list=PLL_nf1OmixTTKhw2oVBtCZUYoMecz-YW5&index=2&t=726s