Either it's him or there's someone else with the same unusual name living a similar life.
There's a passenger list from Liverpool to NY from 8 Sep. 1928 which has a Price Tudor age 45, male, single, who was naturalized in Lockport NY County Ct. 3/1/1904 and was living at 122 Maine St., Ossining N. York. That seems to fit in with the 1884 birth date and what you know about him. There's also an incoming UK list from July 1928 that gives his age as 45, occupation as prison officer, and proposed address as Cefn-y-Bedd near Wrexham Wales.
However, there are other passenger lists that seem to fit more with the 1879 birthdate and the info still seems consistent with your information. There's one from 1938 where he's 58, naturalized in Lockport in 1908, and living at 120 Main St., Ossining. Maybe he changed his age on a whim or genuinely didn't remember how old he was?