Spend the $10 & get the letter. As mentioned above, the computer records are not as up to date as we'd like. They have to pay the staff to take the time to do the records search "the old way" and it costs $$$ to do so. When you think of the millions of guns Ruger has made, followed by the fact that the computer age is still in it's infancy, you can't expect them to have had the time & money to convert all the records to a computer file. I'd bet there are a few rooms filled to the brim with boxes & boxes of old records. It will be a herculean task to ever get them all into a computer database.
But, a normal factory letter on a 3 digit 30 Carbine OM, will reveal it's ship date, and it's correct model info, such as BKH-31, shipped in July 1968. (This is a good example, NOT the actual info.) Now, in the case of the OP's gun, a serial number 2xx is likely a gun that went to a "subscriber" of Rugers. That means the person it was shipped to got all new Rugers with the exact same serial number. When the subscriber program ended, I think there were 500 guns set aside for this program. 001-500.