We present a "super-deblended" far-infrared (FIR) to (sub)millimeter photometric catalog in the Cosmic Evolution Survey (COSMOS), prepared with the method recently developed by Liu et al., with key adaptations. We obtain point-spread function fitting photometry at fixed prior positions including 88,008 galaxies detected in VLA 1.4, 3 GHz, and/or MIPS 24 mu m images. By adding a specifically carved mass-selected sample (with an evolving stellar mass limit), a highly complete prior sample of 194,428 galaxies is achieved for deblending FIR/(sub)mm images. We performed "active" removal of nonrelevant priors at FIR/(sub)mm bands using spectral energy distribution fitting and redshift information. In order to cope with the shallower COSMOS data, we subtract from the maps the flux of faint nonfitted priors and explicitly account for the uncertainty of this step. The resulting photometry (including data from Spitzer, Herschel, SCUBA2, AzTEC, MAMBO, and NSF's Karl G. Jansky Very Large Array at 3 and 1.4 GHz) displays well-behaved quasi-Gaussian uncertainties calibrated from Monte Carlo simulations and tailored to observables (crowding, residual maps). Comparison to ALMA photometry for hundreds of sources provides a remarkable validation of the technique. We detect 11,220 galaxies over the 100-1200 mu m range extending to z(phot) similar to 7. We conservatively selected a sample of 85 z > 4 high-redshift candidates significantly detected in the FIR/(sub)mm, often with secure radio and/or Spitzer/IRAC counterparts. This provides a chance to investigate the first generation of vigorous starburst galaxies (SFRs similar to 1000 M-circle dot yr(-1)). The photometric and value-added catalogs are publicly released.