The real challenge is not to just flip them before war, but also go all the way and integrate them with the last focus before Italy declares on Greece (chances are, you will not be able to hold off the entire Axis that isn't engaged in Barbarossa yet). Since the Italian Greece focus requires the latter to actually exist, this is the task very worth pursuing.
So it was an extremely difficult minmax hell, but I finally managed to do it...beat Italy by half a focus (i.e. they started their War on Greece when I was in the middle of my Balkans integration one). Here's how I did it:
1. You obviously need to beeline the Balkans focus, but it does have a couple blockers along the way...most importantly, these are the ones related to flipping communist. In my experience, you can only afford to take 2.5 non-political foci before flipping or you will be too late, so that's the maximum time you have to sort out your internal situation with factions.
There isn't a real universal advise here except to be very diligent in all your calculations...Very important is to take into account all of the faction loyalty bonuses you'll get from the different foci (because you can't afford to waste PP and time on the faction interactions that you don't need). Start by ONLY doing the socialists until you get the Marxist advisor and then keep working on them until you integrate. Then, bring the Zveno and agrarians to 50 (and not more) to take the Fatherland focus. Do NOT integrate either one of them or destroy the nationalists until you flip because all these things will increase ruling party support and decrease communism...after you do flip, kill the nationalists first because that will also give some bonus to the other factions (again, optimizing your PP expenditure).
2. You've got to heavily invest into spies. I built one MIL to get some rifle production going, but after that only spent my CIV on the spy agency...you don't need to do it day one (since you can't start increasing communism in Greece and Romania until you flip). But you'll definitely need to have a 100% network in both to start boosting immediately after you flip yourself. Also, get a third spy with an advisor or focus, I had two of them boosting and one more changing between the two countries to repair the degrading network.
3. Establish a PP and rifle stock to be able to do propaganda/destabilization decisions without any delay.
4. Even after all of that, I still had Greece and Romania at around 55-60% communism support by the time that I reached the Balkans integration focus...well, this is the risk you'll have to take. Between the 2.5 foci delay in the beginning and two more that you'll have to miss while preparing the Balkan project, you literally can't afford any more delay...So in my case, I jumped the gun and had both these countries go over 60% communism and flip while I was doing the focus and voila.
The rest of the Balkans achievement is a piece of cake after this. Even Italy gave me their stuff peacefully (their code for that event makes them accept your demand if you're stronger, and I already had more fielded manpower than them day one just because of all the units I've inherited from the three nations).