We hear this all the time but the easiest, least risky, most cost effective option is selling your EK1 and buying an EK4 or another B, H or K swapped Civic. Unless you have the passion to do it yourself or are just really attached to your car, it's not worth it. I've spent between 6-7 grand so far on my JDM B18C swap and I still have another 1-2 grand to spend. This is doing it all myself. No labor.
There are quite a few things I'd do different a second time around but I'm not mad about the amount of money I spent because I've learned so much along the way.
Hope that helps a bit.