How about doing it this way: not a tournament, but a free-for-all. Anyone can enter, but they enter without any equipment. Entry fee is a single token, and last individual standing takes all. The arena is the Panic Room, which gets sealed upon the start of the fight, with the happenings within being observed via cameras and recorded. In the middle of the room a pile of random sharp objects is placed for use in the fight.
Anyone can enter?
Anyone. But, just so you know, the Avatar of War
is equipment, too.
Everything on the Armory's list is equipment. Synth-flesh is equipment, amps are equipment, drugs and food are equipment. Basic robot prosthetics are not on the list, by the way, so they are not equipment and are permitted - so synthflesh people can switch out to those if they wish to participate. Custom "free" robot prosthetics' like Lyra's... well, I'd say those are equipment too (at least, other, more powerful Doc's robo-creations certainly are equipment), but maybe in fringe cases this could be worked around (see below for genemods); not that I really expect Lyra to participate, I think she's a bit avert to that sort of violence.
Though it goes a bit against the spirit of this, to forego having to cut out the amps we could merely form a gentlemanly agreement not to use any (and the one who uses is automatically disqualified and, more importantly, considered to be dishonored for they let down the rarest commodity around here - 'Corps trust). Braincases can slide out more easily, so it should not matter.
The real problem begins with genemods, but since those cannot be helped, I can see two solutions: first, if anyone is clearly overpowered compared to others (think Xan the Xan entering such tournament), they are politely refused the right of participation; second, if those genemods are not that powerful at all (like the Fibroblast therapy, or the old-style whatchamacallit-slightly-enhanced-regeneration), it is only fare to let the people fight against basic robots who already have an edge before meatlings. Or, of course, we could say "Nay" to all genemods and insist for robo-people to ride in
civilian-model robotic platforms; you know, the ones that bleed, simulate pain, etc. That'd actually be pretty cool too.
Aaand I think I was really, really ninja'd. But hey, I think I made a convincing point why synthflesh is equipment, but meatflesh and roboflesh (basic) is not!