Sisuitil,
My initial thought was that addition of the Mongolian lands might have come too late to make a difference, however on closer inspection I think you've got an excellent chance at a space race win. In fact you shouldn't even have to resort to sabotage or nuking.
I was initially concerned that Cyrus and HC might be significantly more advanced that the foreign advisor tech screen shows (since you won't see any techs they have which you don't have pre-requisistes for). Then I realized that Cyrus doesn't have Fission, and HC doesn't have Flight and neither has Refrigeration (which they need for Genetics). This makes me think that they probably don't have much beyond what is on the screen now.
The tech screen shows that at your current research rate Fiber Optics, its pre-reqs and Rocketry would take a combined 30 turns. But with some pre-req discounts that you'll pick up, plus increasing contributions from your Mongolian cities, and maybe building Research in some cities it seems that Fiber Optics will be done in 20 to 22 turns. Old Sarai at that point should be able to build the Internet in 10 turns or less, so about 30 turns until you're basically even with the AI in tech.
There's a good chance Cyrus and HC won't even have all the space ship techs by the time you finish Internet. You would be even with them (or maybe ahead

) in starting the most expensive of the parts. They'll have a big lead in building the cheaper parts, but you have enough secondary production cities that can build the cheapies while your best cities are building the big ticket items.
It won't be a very early space race win, but I really don't see any of the AIs coming close. For that reason I would try to stay peaceful until the end. Then again I may be wrong and Cyrus may be more advanced than I surmise (I don't really consider HC a threat at this point because of limited production and no aluminum).
A couple of little things to think about when you restart: I would emphasize growth in Old Sarai for a while. Its only at size 11 at this point and it needs to grow to 18 to make maximum use of its tiles. If I calculated right its capable of over 60 base hammers at that size

. Also I noticed that a couple of Karakorum's towns got assigned to the little city to its north even though that city has no commerce multiplier buildings

.