Minimum Necessary Techs:
Meditation or Polytheism
Priesthood
Writing
Monarchy
Priesthood is really key here, as it is a common prerequisite for the Oracle, Writing, and Monarchy (although there are other ways to get Writing and Monarchy, why not synergize?). I would start building the Oracle after researching Writing, making sure you finish Monarchy before the Oracle is completed.
I suppose you could beeline all of this, but it would be smoother to get most of your worker/military techs in before you go for Monarchy. At a minimum, I would want at least one solid food tech (fishing, agriculture, or animal husbandry), the wheel, pottery, mining, and bronze working. If I was trying to get early longbows from feudalism, I'd throw in hunting and archery early too.
The Protective civs are an obvious choice with feudalism-enabled free promotion longbows. Charismatic is also handy for cheap promotions. Some longbow comparisons, assuming Vassalage, Theocracy, and a barracks:
Churchill (Prot/Char): CG I, Drill I, two other promotions (7/8 xp)
Sitting Bull (Phil/Prot) (with totem pole): CG I, Drill I, three other promotions (10/10 xp)
Other protective civs: CG I, Drill I, two other promotions (7/10 xp)
Other charismatic civs: two promotions (7/8 xp)
In these examples, Theocracy only immediately benefits Sitting Bull; with just Vassalage and a barracks, the other civs still get 5 xp which is enough for two promotions plus any freebies from Protective. A Sitting Bull CG I / Drill IV longbow at 1000 BC is nothing to sneeze at, however.
Getting Theocracy going requires an additional minimum investment in Masonry, Monotheism, and Theology. Theology would be a worthwhile Oracle slingshot in itself if it wasn't for the fact that we're going for Feudalism here, which is the more expensive tech (by 200 beakers).
Shwedagon Paya is a pretty bad choice for this gambit I think.You can get theocracy by beelining Aestetics after Monarchy (Not sure what other techs you need) and building the shwedylon Palace rather than the traditional monotheism/theology route. You can also lightbulb theology with a prophet if you can generate enough GP points.
If you've gone after a Feudalism slingshot, you probably have 2 cities. It's doubtful that you'd have 3. You can probably expect ~10 hammers per turn on average: ~ size 4 working 2 mines and some whipping thrown in. So you could build ~5-10 longbows in those 25 turns before you bulb Theology. That's enough units/time to start a crusade and take a capital. Your reinforcements can then be built with Theocracy's XP bonus - except around that time you'll probably get your first Great General.
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Longbows are terrible attack units, no city raider, about equal base offensive str as a swordsman. While you are making the beeline your economy suffers
I truly do not understand this slingshot, and will rarely build an archer let along a longbow.
If you want the same experience on your units, simply start some ancient wars and pop 2 ggs, boom there you go put them in your main millitary city, and the same exp granted by millitary civics without being forced to harm your economy.
Longbows are terrible attack units, no city raider, about equal base offensive str as a swordsman. While you are making the beeline your economy suffers
I truly do not understand this slingshot, and will rarely build an archer let along a longbow.
If you want the same experience on your units, simply start some ancient wars and pop 2 ggs, boom there you go put them in your main millitary city, and the same exp granted by millitary civics without being forced to harm your economy.
Would you rather have a CR1 sword or a Drill 4 longbow? Personally I'd take the drill 4 longbow. Or the drill2 cover+shock longbow makes a pretty good city attacker since defenders will be vulnerable to either cover or shock.
I'd only do this if I have the right leader and a Great commerce Start, possibly a gold mine in my FC.
It makes The beeline a lot smoother and the rush a lot quicker.