Variants that are older than Modern Standard Chess

I understand that Modern Standard Chess is not the oldest chess variant, with Shatranj being the ancestor of Modern Standard Chess.  I know that there are other chess variants that were invented before modern standard chess such as Tamerlane Chess, Courier Chess, and Chaturanga.  From what I understand there were other variants of chess that were invented before modern standard chess, in addition to the ones I just mentioned, including some that were played on boards that were larger than an 8 by 8 board.  I tried using google, but still couldn't find the other chess variants, and find that finding the names of variants I don't know the names to in a search engine is very difficult, if not impossible.

Does anyone know the names to some ancient chess variants, older than modern chess, that I didn't mention?

I have a book from the late 60's -- Chess Variations: Ancient, Regional, and Modern that has a number of versions listed.

TOC:

I am not sure what counts as the invention date of the current Mad Queen variant (= FIDE Chess). In the middle ages Chess rules were not universal, but there were various regions in Europe, each with their own rule variations. The last rules to settle down were probably those associated with castling, e.p. capture and promotion choice (or perhaps the move of the Queen?).

That being said, large historic variants that are pretty old are Sho Shogi (9x9), Chu Shogi (12x12) and Dai Shogi (15x15), which were around AD 1350, and their poorly known precursors Heian Shogi (9x8 or 9x9?) and Heian Dai Shogi (13x13), all from Japan. Of course there is Xiangqi ('Chinese Chess', 9x10), which is pretty old, and of which some even claim that it predates Chaturanga, and is the true ancestor of all chess variants. Grant Acedrex (12x12) from the Spanish Alfonso codex (AD 1283?) is a European variant. Carrera Chess (AD 1617, Italy) is a 10x8 variant similar to Capablanca Chess, which was apparently invented before the invention of castling (as it has none).