I don't know about the Atomic strat. I don't think it's possible. Fractal makes it even crazier to attempt.
I do think two cycles is possible with a bit of luck but it won't be easy. I would aim for a T230 or so finish, so that means founding congress around 160? I think the only way for this strat to work is to bulb your GS in waves, maximizing their science output for the era that you are in. I would do something like this:
After Education research Astronomy first and then go all the way to Architecture and build PT before Printing Press. At least an early PT could translate into an extra spawned GS so it is not that bad of an idea. At this point with one city and only settling one GS I think you will naturally hit PP around T160 which is perfect.
Now the race is on. You probably want to bulb at least 1 GS immediately then Oxford into Scientific Theory with enough money to rush buy a school. That way it won't be delayed by much at all even though you hit a late PP. 8 turns from then you can bulb another GS to get into Modern era.
At this point you are looking towards Statue of Liberty and Research Labs (assuming you chose Freedom, which I think is the best). It might even be worth trying to complete Rationalism to use the free tech for Plastics... it depends how many GS you have saved, and whether or not an early lab will spawn an extra GS for you.
After that it's pretty simple- do whatever you need to hit info era by T220 to initiate vote and then you have 10 turns to complete Globalization which is the easy part. You will need to faith buy at least 2 GS for this to work, maybe 3. It's roughly 50k beakers to go from Plastics > Telecommunications. With a combination of GS and RAs it's possible.
You will also need to propose and pass something useful on first vote, either Sciences Funding or Cultural Heritage Sites. Then on the second vote you can propose World Ideology with no diplo penalty. The real danger of delaying PP is not delaying schools, but that you risk missing out on LToP, which is an essential wonder here IMO.
You can safely get banking, acoustics and architecture before PP, and the ingenious thing about this is you'll get a bunch of free techs from spying on the AI. Since you'd have ignored the bottom part of the tech tree you'll get about one free tech every 3-5 turns after hitting rationalism. I have always been thinking the early observatory has been a must have, and slow building the university + oxford will usually take as much time as getting sailing optics and compass.
While you get as many techs you need towards scientific theory, your spy will be level 3 and have grabbed you most of what you need to get PP around turn 160-163 as long as you had a good starting location with lots of food. Desert hills are great, but after a few tries, I find the real key is having high yielding food tiles so that you can actually work as many tiles as possible by the time you've got your UIs up - and always fill your specialist slots (except merchants, of course - you don't want to pop a great merchant and delay a GS, depending on your production, popping one or two GE can be worth while, but it is situational).
Finishing rationalism for plastics has never been a problem for me. Since there are not a lot to build between the observatory and public schools other than the forbidden palace and, depending on your RA timing, the PT (and obviously the LToP) and you won't be in a rush racing the AI for either PT or LToP, picking up all the guilds, the amphitheater and an opera house unlocks a very early hermitage, and it being an OCC it should only take a couple of turns to build, and you won't have to worry about culture much after that.
I totally agree with the GS beaker timings. Where I feel the most unsure about all this is if oxford should be used for astronomy (I think so in most games, you will most likely need it to find the last few AIs and a bunch of CSes) or saved for ST. The biggest leaps in science production throughout the game seams to be:
( 0) Faith pantheon - probably desert folklore - this for faith buying GS end game)
1) (Great) Library
2) Rapid population growth early game
3) NC
4) first (and only) academy improvement
5) Education (universities + specialists)
6) Astronomy (observatories)
7) Rationalism (first Secularism, then I'd go with the right track before left to spawn that extra GS down the line - 1 GS will pretty much always be way better than an RA, even with PT and SR)
8) Public schools
9) Great Scientists generation (wonders (LToP, PT,) Avant Garde tenet etc. - maybe even a wonder that gives flat bonus to GS if you have extra production cyscles and nothing better to spend them on)
10) fast population growth from Civil Society
11) Research Labs
12) More population growth
( 13) Production improvement e.g. Statue of Liberty - after this point you really need to decide if any additional improvements are going to help you or if you should just convert production into beakers)
I wrote them in the order they come naturally in most games. At some point either just before rationalism or after finishing it, you will probably want Scholasticism - situational read; if you have lots of high pop CS allies; it could even be a priority above finishing Rationalism early (but make sure you will still get rati finisher before too late). Whenever using a GS will make a new science improvement (public schools, research labs) available in the next turn, or you are about to finish rationalism and using that GS would make your free tech a higher tier one - that is when I'd use my GS (and of course use them to secure Information era and Globalization late game).
My main issue is still how low the AI science yield gets on Emperor and how it really destroys the value of RAs. I am thinking that counter espionage should only be used if you are desperate to level your spies - you will want the AI to catch up on the tech for the RA value. Since you will be bee-lining tech for most of the game you should be able to steal some low value techs with your spies instead to level them. I need to experiment with the GS beaker value a bit more - if you only need one to get from PP to ST in one turn, I guess that would be optimal.
Talking about spies - as long as you are not to worried about being best friends with Alexander & co. for the purpose of RAs, a semi-early NIA can save you a lot of gold from CS bribes (this is most likely obvious to you, but there might be more people reading the thread).
One think that I will need to experiment with is ignoring tithes as founder and grabbing Interfaith Dialogue + cheap missionaries. I hate seeing 1300 or so faith wasted on the 500 and 800 prophets (sometimes even a 1200 faith one if I get a lot of religious CS allies early) and there seem to be some very aggressive AIs in the religious game here. I'd simply buy as many missionaries I could pre-Renaissance and then maybe one or two when I am about to pop a prophet in Renaissance era. I should only have to piss off one AI this way, and it might be worth it. 3 GS seems to be about as many as you can expect to buy from faith either way, so as long as you make sure to be able to save up 4k faith by the end game (not hard at all if there are a few religious CSs left on the map and you've got a great desert with folklore), the missionaries would be the best way of turning excess faith into beakers.
As a side note: My understanding of the civ 5 mechanics and strategies has improved immensely by the last couple of gauntlet challenges. Playing at anything but Diety now seems far too trivial in a regular SP game.