The main lore problem with this concept though is that it was specifically stated that the magitek armour's weapon systems are permanently broken due to Cid, Biggs and Wedge substituting an Eorzean mammet heart in place of a necessary Garlean component - Jessie did all she could to restore the weapon systems online but all it did was make them for show, they cannot actually deal damage. The Ironworks lack the components necessary to repair a magitek armour to full power (that's why they had to use the mammet heart in the first place), so upgrading it just wouldn't be possible I'm afraid.

However, I admit this idea would be fun, but I think rather than just concentrating on the magitek armour, some kind of mount jousting would work better (because, after all why just concentrate on the magitek armour? We have a wide variety of different mounts, why cast all them aside just in favour of one particular one?). Either way, your idea with a bit more tweaking could be really fun.