With that much recoil involved I'd say the structures of the gun mounting and/or the howdah would go first.
Anyway, it's a given even in a fantasy version the artillery piece would be from a very light end, to keep both its weight, recoil, and powder consumption in check. One would expect a thin-walled type of gun designed for firing stone and grape shot (which are light and hence get off with fairly small propellant charges, ergo fairly little pressure build-up in the chamber ergo the gun can be made fairly light), or something akin to the light field howitzers of Europe (designed for firing explosive grenades, which being hollow are light for their size, and "case" shot - a variant of grapeshot).
Also, given that there would be uncomfortably little working space in the howdah, it'd probably have to be of the breech-loading type. While those are quick and convenient to reload - since the separate chambers can be pre-packed and swapped quite quickly - they had some issues with propellant gas leaking from the join between the chamber and the barrel, which would further reduce the recoil... Incidentally this design was abandoned from larger pieces fairly early, but remained common enough in small antipersonnel swivel-guns and the like where the pressure-loss issues mattered fairly little.
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