We present a new technique to measure multi-wavelength "super-deblended" photometry from highly confused images, which we apply to Herschel and ground-based far-infrared (FIR) and (sub-)millimeter (mm) data in the northern field of the Great Observatories Origins Deep Survey (GOODS-N). There are two key novelties. First, starting with a large database of deep Spitzer 24{mu}m and VLA 20cm detections that are used to define prior positions for fitting the FIR/submm data, we perform an active selection of useful priors independently at each frequency band, moving from less to more confused bands. Exploiting knowledge of redshift and all available photometry, we identify hopelessly faint priors that we remove from the fitting pool. This approach significantly reduces blending degeneracies and allows reliable photometry to be obtained for galaxies in FIR+mm bands. Second, we obtain well-behaved, nearly Gaussian flux density uncertainties, individually tailored to all fitted priors for each band. This is done by exploiting extensive simulations that allow us to calibrate the conversion of formal fitting uncertainties to realistic uncertainties, depending on directly measurable quantities. We achieve deeper detection limits with high fidelity measurements and uncertainties at FIR+mm bands. As an illustration of the utility of these measurements, we identify 70 galaxies with z>=3 and reliable FIR+mm detections. We present new constraints on the cosmic star formation rate density at 3<z<6, finding a significant contribution from z>=3 dusty galaxies that are missed by optical-to-near-infrared color selection. Photometric measurements for 3306 priors, including more than 1000 FIR+mm detections, are released publicly with our catalog.