The "Model 1898" rifle was made from 1898 until a VERY few in 1904, so there is NO inconsistancy with that marking vs. that serial number. Most original carbines made during that time period used receivers stamped "Model 1899" - and they occur in several well-defined blocks.

The true "Model 1898" carbines are a fairly rare, and hard to ID, item - but - the few (just 5003) specimens made occur in the 112xxx to 135xxx range only, which is close to the beginning of the 1898 model style. Yours is thus way out of line, with zero possiblity of being an original Springfield build. Sorry to give you the bad news.

As to the long ownership, yesterday's "collectors" were nowhere near as sophisticated and well-infomed (due to the several books now available) as those buying guns today. Time was, if something looked nice, and had a short barrel, it was a "carbine". That situation no longer applies.