Honestly, as an outside observer, it sounds to me like you've already made up your mind in favor of SPIA! Which, for what it's worth, does sound to me like the right move. I also was fortunate enough to get accepted to HKS with full funding, though I got rejected from SPIA; if I'd gotten in, however, I would have gone there over HKS. The brand names of the two schools are basically equally strong in the public policy space, and the curricula are pretty similar as well (unless you're interested in something pretty niche and/or would want to take non-HKS classes while you're at Harvard, which don't sound like the case for you). So, even if you do decide you want to enter the private sector down the line, the skills that you'd gain at SPIA would likely set you up the same as HKS. So all in all, the difference in funding seems to me to be significant enough, and the differences in programs negligible enough, that SPIA seems to me to be the way to go.
And huge congratulations on getting to make this choice!