We present a new technique to obtain multi-wavelength $\textit{"super-deblended"}$ photometry in highly confused images, that we apply here in the GOODS-North field to Herschel and (sub-)millimeter data sets. The key novelties of the method are two: first, starting from a common large prior database of deep 24 $μ$m and VLA 20 cm detections, an $\textit{active}$ selection of $\textit{useful}$ fitting priors is performed independently at each frequency band and moving from less to more confused bands. Exploiting knowledge of redshift and all available photometry for each source up to the dataset under exam, we identify $\textit{hopelessly faint}$ priors that we remove from the fitting pool. This approach critically reduces blending degeneracies and allows reliable photometry of galaxies in FIR+mm bands. Second, we obtain well-behaved $\textit{quasi-Gaussian}$ flux uncertainties, individually tailored to all fitted priors in each band. This is done exploiting extensive simulations calibrating the conversion of formal fitting uncertainties onto real uncertainties, depending on quantities directly measurable in the observations. Our catalog achieves deeper detection limits with high fidelity measurements and uncertainties at far-infrared to millimeter bands. We identify 71 $z \ge 3$ galaxies with reliable FIR+mm detection and study their location in stellar mass--star formation rate diagrams. We present new constraints on the cosmic star formation rate density at $3