"Specific questions - could a stock cartouche SWP/1883 be correct for this rifle? If I'm interpreting some online databases correctly, the serial should date to 1884"
No Problem!
According to Frasca & Hill, "The 45-70 Springfield" - a very authorative work - the designation on the receiver was only changed from 1873 to 1884 in fiscal year 1886.
The number 237815, according to the same source, would put it in the 1st quarter of 1884. However, bearing in mind that the quoted "end of year" serial numbers are estimates related to calendar years, I wouldn't worry about it. Maybe someone can explain what exactly the fiscal year period was?
Later: it appears that the US fiscal year runs from October to September of the following year. Since the fiscal year is designated according to the calendar year in which it ends, not when it begins (!), rifles made from October-December 1883 would have been attributed to fiscal year 1884.
I would guess that in old records this may lead to some statistical confusion. Like I said, don't worry, it looks like a proper Trapdoor, even if the bean counters caused confusion with the calendar!