Colt worked around S&W's patent with the Thuer conversion; it was a lousy conversion and not real popular. After the patent expired, the Richards conversion was used (designed to use up old parts!). When they ran out of some of the parts, they went to the Richards-Mason conversion. Eventually (actually, this all happened in a few years!) the factory did a re-designed purpose-built cartridge version of the 1860: the 1871 Colt aka the Opentop. Production of one model didn't stop with the introduction of the next model--gotta use up parts, ya know.
But as for if Colt ever offered the conversion as a service. . . they did convert revolvers for the gov't, at the rate of ~$3.50 per. Some people apparently were able to get conversions done at the factory, but I'm unsure if they "knew a guy who knew a guy" or if it was a service offered by Colt. Everyone and their dog was doing conversions for a while, I've seen old ads offering the service for $2.75. Used C&B revolvers were fairly cheap after the Civil War, new price on an 1860 was about $14.50 in 1865. Colt charged the gov't $13.50 for the 1873 P when it came out.
Remington actually started doing conversions earlier--early enough they had to pay a royalty to S&W for the use of the bored-through cylinder. Conversion cost (for a dealer, in a large quantity) was ~$3.50, with S&W getting $1 royalties. Cartridge was a weird .46 cal rimfire, old stories I heard suggest that it would also fire the .44 Henry as long as you didn't expect to hit anything past spitting distance.