Yes, your analysis is accurate. I'm also impressed with the historical background. However, I don't believe this example illustrates the difference between an 8x8 and a 10x8 board for Rook endgames (if, in fact, there is any difference). A Lucena position, according to my sources, is a position where the White King is on the last rank, directly in front of his Pawn, and the Black King is off to one side of the Pawn. As you pointed out, the standard winning procedure is to "build a bridge" as in the line you gave. This is the same on either type of board, as long as the Pawn is not on a Rook file. The other position (White: Kh6, Ra7, Pg6; Black: Kg8, Rb8) is called a "passive defense" rather than a Lucena position and is a draw if White's Pawn is on a Rook or Knight file, and a win for White if the Pawn is on a Bishop or central file, with the winning procedure exactly as your "Gothic" line. However, "passive defense" is still a draw on a 10x8 board if White's Pawn is on a Knight or Rook file (a, b, i, or j) and this is no different than on an 8x8 board. My point is that it appears (to me, at least :-) ) that the Rook endgame theory of the 8x8 board carries over "mutatis mutandi" to the 10x8 board. In fact, I can't think of any other endings that depend on the geometry of the board (10x8 vs 8x8) the way a K+B+N vs K ending does.

An interesting question in this topic is whether either a K+A+P vs K+R or K+R+P vs K+A is a win (or, under what conditions either one would be a win).