> Since this wooden rod travels several miles in a 6 second time frame - traveling more than 500M/s on average - don't we have to assume it accumulates?

The basic assumption here is that the rules as written beat physics and common sense. When you play that game, you have to do it rigorously. You can't say that rules trump physics one moment, and physics trump rules the next.

> There's also the rule of cool. If it makes the story better/ more enjoyable: have at it.

That does rule out the Peasant Railgun more thoroughly than any rules argument.