According to Jay Miller's 1985 TAR article updating Shellabear's work, the straightline cancel COSTA RICA does exist, designated #P-1M. Perhaps a different ship from the one in your link, but with the same name.
At least one "COSTA RICA" exists. It was in Siegel's Sale 937 Lot 327 2007 Rarities of the World: The Henry Tolman II Collection of Pacific Mail Steamship Co. Cancellations on Revenue Stamps. The incomparable collection of scarce to rare PMSS Co. straightlines on a wide variety of First, Second and Third Issue Revenues, arranged by line and name of ship, comprising: Atlantic Line "ARIZONA" (8), "HENRY CHAUNCEY" (12), "OCEAN QUEEN" (13, incl. rare use on 25c Second Issue, reported by Mr. Tolman to be the only known 25c of any line), and "RISING STAR" (17); Shanghai Branch Line "COSTA RICA" (1); Pacific Line "CONSTITUTION" (1), "GOLDEN CITY" (2), "MONTANA" (5), and "SACRAMENTO" (2); China Line "ALASKA" (10), "AMERICA" (6), "CHINA" (4), "COLORADO" (2), "GREAT REPUBLIC" (4), "JAPAN" (11) and "OREGONIAN" (3); also includes a few ancillary items such as stamps with blue PMSS circular datestamps, document and uncancelled check, almost all stamps have small faults but have been chosen for clear strikes (many straightlines struck more than once on each stamp); as is well known to Revenue specialists, the PMSS Co. cancellations are highly prized and generally sell for $75-100 for the more common types to $300-400 for the scarce markings, this offering of 101 examples is unprecedented, but to preserve Mr. Tolman's achievement and give others the opportunity to expand upon it, we are offering the collection intact -- we are also hoping that transoceanic mail specialists will look at this collection in the Rarities sale, whereas they might overlook it in a Revenue stamp sale.
It went for $35,000 on an estimate of $5,000-$7,500.
Link here: http://www.siegelauctions.com/2007/937/937.pdf