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You definitely need the multiplier or it would take you months to get that much afky power.
The good news is that you don't specifically require long rebirths to get your multiplier up, as long as you continue to do the afky thing in every rebirth (a ratio of 5:1 between HP and count works just fine in most cases), you can expect to multiply your multiplier by 2-3 each month.
This might not sound that big, but it is multiplicative, meaning that in a month you would be at least to 10, then a month later to 20, 40, 80 and so on.
There are of course ways to accelerate it but for the most part it's more about being consistent with it over a fairly long period of time.
The good "lazy but it works" method is to actively grind it at the start of a rebirth until your HP is around 2k (and count to 1,000), put your exp into speed until you reach 3,800 (the cap for it) and continue to raise your HP and count at a ratio of 5:1 (4:1 would also work in the begining but it's easier to remember the ratio if you keep the same over the months), and once in a while during the rebirth coming back to spend the exp (use the "cap" button on power and if it reaches the cap spending in HP and count again).
Right before rebirthing, you want to sink any leftover exp into afky power (use the "max" button) just to get a bit more.
The best thing is that it works regardless of your rebirth length, it works in the very short rebirths (someone even did a lot of extremely short rebiths just spending on afky power and rebirthing over and over, very tedious to do properly and he made absolutely no progress in anything else but it worked very well), might rebirths as well as very long ones like AAC, UAC or PMC.
As for the reasons why you really want the multiplier, there are two.
The first is as mentioned above, the exp cost for that amount of power is very high, and the cost of HP and count are also growing very fast.
The second is that your afky clone pet is going to be very weak in campaigns unless you reach a very high afky power in that rebirth.
If your plan is to send the clone in dungeons it won't matter much but you also need an insanely high afky power if you want to evolve that pet (and his evolution bonus is in campaigns, which goes very well with his campaign bonus when you have high afky power).
You need +20% boost to campaigns, right now I am at 14% with an afky power of 21 E+12, and that is with a multiplier of 1.372 E+6 (E+6 means million in case you are not familiar with the notation) and a rebirth of 28 days (I'm not trying to evolve the pet, but even if I wanted it would take me forever at that multiplier).
1 extra percent means doubling the amount of afky power so I would need to multiply my current power by about 2^6 = 64 (yes, that would mean not rebirthing for over 3 year while continuing to frequently spend afky exp if I didn't raise the multiplier).
The good news is that run helped me get a few more pets by killing higher P. Baals, but it was a huge inefficient block of time. Now that I'm doing a lot more reading about strategy, etc., I'm making much better choices.
At least with 6 months without rebirthing you should have been able to implement the "idle GP generation", with black holes, god crystals and god power campaigns, and you could probably unlock a lot of the p baal pets, but after a 3 months long rebirth I can't say I envy you, it is incredibly boring when you have months where you more or less only come back twice a day to feed your pets and restart campaigns.
How much afky power do you need to reach +20% campaign bonus, AND, does that include walking stick bonus in order to evolve Afky Clone or no?
And sure enough log2(1.126e15) = 50 (well, 50.000128250.... so close enough)
Since it starts at -30 you need those 50 to get to +20.
As far as I know only the campaign bonus from afky counts but I had evolved him before the walking sticks were even remotely an option for me (I'm not even sure if they existed yet back then).
1.126 quintillion?! That number sounds like a lot of fun.... >_>;
I can usually get 700m+ power in a 24h hour run now, but it depends on if I pay enough attention to it. I got 1 billion power in my last 24h run on a day off.
If you pay a lot of attention to AFKY (especially at the start of a rebirth) you can multiply your exp muliplier between 2 and 6 each month, after a couple months it becomes an automatism to quickly set things for it right after a rebirth for a minute or so and then every now and then spend the exp.
Thankfully now the pet should always have the campaign bonus from the highest afky power reached instead of the current so you won't be losing anything from rebirthing.
That addition was a bliss. Also, the game always 'click' on Max power button for you before rebirthing. So, setting things up on the beggining is always good, even if you forget about it later. Found this by luck, and have no idea when it started.
I don't know about the stick either (I've been lazy about dungeons / gear / evolutions and don't have many sticks on non-adventurers, and the sticks (all of my gear in general, really) that I do have equipped are still just T1 crap anyway, and the thought hadn't occurred to me to wonder if I could use a stick to cheat this pet's evo condition), but I evolved my afky pet fairly recently and the thing that I had observed about it was that the evo condition needed me to have high enough afky power in that run. It didn't actually care about the bonus, which was secured by my highest afky power ever reached before. I had previously set a personal record for afky power that was worth something like +23% for the campaign bonus, but when I had realized that I had enough materials for it and tried to evolve it the game said that I hadn't met the conditions. I tried again later, after I was able to increase my afky power in that run a bit, and the evo worked.
Edit: I think the sticks, hammers, and pots have all been present since dungeons and evos were first added to the game. The knives and the training swords were each added in different updates later on, if I recall correctly. Let's see... The knives are mentioned as being added in the patch notes for Aug 7 2019, and the training swords are mentioned as being added in the patch notes for Feb 20 2019. The pet dungeon update itself went live for all players on Jan 7 2019 (although people had been playing for about a month before that if they enabled the game's beta branch on steam).
It can suck up quite a bit of resources though to forge / reforge and upgrade an item and then to maybe repeat the process for the next tier version of that item. Which looks especially bad when you're hoping to stockpile those materials for pet evos.