I'm a bit confused by your terminology and I'm not a DSP guru, but as far as I understand it, if you want a sinc filter where the coeffs sum to exactly 1, you pretty much want Lanczos, because that's pretty much what Lanczos is. Getting the coeffs to sum to exactly 1 in a real implementation (of any resizer) with all its pesky numerical precision issues requires dithering them though, and even then there might still be a small residual error. See for example
zimg's take on it.