This is probably a little bit too late, but in case you still want an answer, I would advise not to open Rationalism because it's too late for that, and by the time it pays of the game should be over. Instead finish commerce for the extra boost on gold and happiness.
I would proceed to take Lisbon, or Honolulu (or both with 2 armies). And in the mean time complete a road through that rough terrain towards India. Amsterdam looks like it will be the hardest, but if you get Rotterdam first and then place a couple of citadels to grab that road you will manage to take it fairly easy.
You need to plan ahead and build roads towards the civs you want to take, so a road towards Delhi, and even one towards Honolulu would help.
Tech wise you could go for radio with oxford to get ideology (autocracy is probably best). You could also get ideology with industrialization but that means you will not be able to build your UU, so I would delay that (but as another benefit you get to build the Big Ben so if you have the time for that you could do it for an incredible reduction in purchasing military). You might also need chemistry to finish the last civs. If you have autocracy with purchasing discounts you can buy yourself a nice army of cannons very fast especially if you faith buy a Great Merchant.
I think that you can finish it with these techs alone so there is really no sense in getting rationalism. Just bulb your current GS to get these techs. If you have enough GS you could try for ST then Electricity and Radio with oxford. Otherwise just get industrialization and rush buy 3 factories. Chemistry will be next.