Just want to say that I finally finished my Jihad Achievement, in 1758, the night 1.5 came out. I probably could have added way more provinces, but worried that my relations with my PU Nogai whom I fed over 50 provinces (with potentially many more to come) might dip permanently below 190, and indeed I already had -25 Great Power penalty, I decided to just start integrating them outright. Indeed after starting integrating the next month I think there is a -75 penalty of some sort... but anyway, integration finished in 1754 or something, but they still had several non-Sunni provinces. Conversion finally finished in 1758 and I finished with 533 provinces. Not gonna bother continue the game. It was mostly a grind after you become sufficiently powerful.
My OE was essentially between 100% and 200% starting around 1630, usually around 150%. Above 200% rebels are really annoying, just way too many of them. So many that in fact I was losing manpower! So after that I made sure never to exceed 200% again. Once in a while I dip below 100%, but I don't know if it resets any counters.
I don't know if PU feeding is still viable in 1.5, but Nogai my PU had a balanced personality throughout, and bought lots of provinces from me. Importantly, lots of 5 and 6 base tax provinces. I also managed to get a westernized Pattani as vassal (all small countries seem to eventually decide to westernize, so this is something almost guaranteed to happen, i picked up lots of vassals this way), which I them fed all of Aceh and Brunei and the other Malay country when they happen to have a militaristic ruler. In my late game, i.e. after annexing Xi, Zhou, Shun, taking pretty much all Indian provinces, it was quite easy to get small Sunni countries as vassals, such as Iraq, Tripoli (is that right?), and Algiers, since they all felt threatened. So not as much conquest as necessary by the game's end.
As I have mentioned much earlier in this thread, I didn't stop Russia early on. My approach was not going for the Siberian bottleneck; I picked Diplo, Defensive, Expansion and took stab hits to invade and annex Indian and Asian countries. They gave me cores all the way to Korea before I westernized, making sure to pick up the crucial Chinese factions as vassals. My game was far from perfect, as it was my first real EU4 game where I diplo-annex on such a huge scale, so at one point I have 13/8 diplo relations, with some redundant and unnecessary vassals. If I had to do it again, I might pick Explore instead of Expansion as my 3rd idea, or even 2nd instead of Def.
Russia was dealt with much later. I had about 10 colonies that I managed to establish in Siberia East, and essentially fought all the way west. Those Russian 10 year coring times are annoying as hell. Lots of revolts. I ended up spending dip point to culture convert some of my takeover of Russia's Siberian provinces because I hate dealing with revolts.
For my 7th idea, I picked Explore, just for fun. And indeed having an extra colonist makes colonization much easier. The +33% settlers increase also helps a lot. So yeah, Explore is a good idea to pick for this achievement.