The hot Big Bang may have emerged from evaporation of primordial black holes (PBHs) lighter than 10^9 g. Standard monochromatic treatments predict nearly simultaneous evaporation, abrupt reheating, and a large Poltergeist scalar-induced gravitational wave signal. We confront this expectation with the irreducible collapse mass tail predicted by general relativity, dfPBH/d ln M proportional to M^3.78, which smooths reheating, suppresses the signal by orders of magnitude, and reopens the ultra-light PBH window.