The main benefit of getting these seems to me to be not the potential 3% increase in prestige multiplier, nor the effect on golden cookies, but the boost to the effect of Golden Switch. These three upgrades are counted in Residual Luck's effect on Golden Switch, bringing the number of such upgrades to 9, and increasing the potential GS boost from 2.1 to 2.4, i.e. an increase of 14%.
I managed to get these "hidden upgrades" in both the live and beta games, after a lot of frustration and missed opportunities, and a lot of staring at the screen. Later on I realised I could have done it with less stress by doing some fairly simple calculations.
To get all three of them - and you may as well get them all at once, since the condition for the third one implies that the conditions for the other two are satisfied - you must ascend with a prestige value ending in 777,777. That requires noting your exact current prestige (turn off short numbers), and then calculating what extra prestige you need to get on this run. If you are at this level of the game, the prestige will be increasing so fast that it's impossible to pick the exact moment to ascend unless you slow down the production by selling buildings. You don't want to do this too soon, though; you want to wait until you are fairly close to the desired figure before selling things off, otherwise you spend hours staring at the screen waiting. The temptation to speed things up by clicking cookies or reindeer, casting Conjure Baked Goods etc is almost irresistible, but do it at the wrong time and it will take your prestige just over the limit, forcing you to wait for another million prestige points to accrue.
If I were doing it again, I wouldn't spend time and nervous energy trying to speed up the process of getting to the point when I can shut things down. I'd just leave it idling, having done a rough calculation of when the prestige would be close to the required value so that shortly before that time I could start slowing down the production. I'd probably leave golden switch on and be in a season other than Christmas so I don't end up accidentally clicking on cookies or a reindeer. The wrinklers can stuff up the calculations mightily, so I'd have Elder Pledge, or perhaps even sell all the grannies, which seems the simplest way to stop the wrinklers spawning. All of this makes CpS a bit less than it could be, of course, but you only have to do this once, for one run.
OK... to calculate how long till the prestige reaches the correct value:
Current prestige (from previous runs) = Pc Extra prestige so far this run = Pe Prestige if I ascended now = Pc+Pe (call this Pn) Additional prestige to get Lucky Payout = (777,777 - Pn) mod 1,000,000 = Pa Prestige on ascension with Pa = Pn + Pa = P (this will end in 777777) Ascend when the number in the prestige counter equals P - Pc.
Extra cookies required = (P^3-Pn^3) * 1 trillion Divide this by current CpS to estimate the time.
Current prestige = 111111111 Extra prestige so far this run = 222222 Total prestige now = 111333333 additional prestige required = 444444 prestige on ascending with extra = 111777777
extra cookies required = (111777777^3 - 111333333^3) * trillion = 1.647 undecillion Current CpS = 470 nonillion
This gives waiting time of 3505 seconds or about 58 minutes.
So at about the 55 minute mark I would start selling buildings and watching the prestige count to pick the right moment. The number to watch for in the counter is 111777777 - 111111111 = 666666.