I have struggled with choosing film for pinhole photography for a while. I have used a lot of Kodak Plus-X, which is remarkably similar to Ilford FP4+. The cool thing is that its reciprocity problems start at about 1/2s. So at 1/2s metered at f/138 (my camera aperture, what's yours?) I shot at 1s, and at 1s metered I shot at 2-3s. This way I got exposures long enough to control with the manual shutter mechanism.
But then it gets dark, and a 15s metered exposure all of a sudden requires several minutes of exposure, and as it gets darker it gets worse.
So, I ended up debating how to solve this, and I have decided on Kodak Tmax 100. It's a film of the same speed as FP4/Plus-X in daylight, yet its reciprocity characteristics are pretty stable down to about 2 minutes, meaning I don't have to compensate much until it's really dark out, in which case I'd dig out a different camera with a larger aperture. That gives me the greatest lighting flexibility.
If it's really dark and I'm not in mid roll, I can also use Tmax 400, which will allow me roughly the same reciprocity characteristics but with two stops added speed. ISO 400 does not work for me during daytime, though, as I require a 1/4s exposure for that and I can't do that accurately.
So, Tmax 100. Fuji Acros would be another excellent choice as its reciprocity characteristics is (unbelievably) perhaps even better than that of Tmax 100.
I don't know what the reciprocity characteristics of Neopan 400 is. You'll have to test it.