I hope this isn't considered very bad form to suggest but:

Seriously I would try using yojimbo. If you can build a good relationship with him (see the FAQs on this) then you can kill Eartheater in a short time with minimal effort.

Simply wait for yojimbo to do zanmato (Use Yuna's Great Summons to make sure he has full over-drive as this will seriously increase the chances). You can afford to pay him a decent sum (say between 5-15,000 gil) because you can often loot earth eater for items worth 50k, sometimes even 150k gil (or just keep the triple overdrive/auto-potion 3 slots if you like). Paying him more will increase the chances of zanmato and probably save you time and ultimately earn more gil.

If he loses, (doesn't do zanmato) don't save the game (it will screw up your relationship with him). Just reset and try again. If you're on the right lines, he will win roughly 50% of the time. Get Yuna's overdrive up again (that triple overdrive will help!), rinse and repeat.

The only downside is you will never get an overkill, therefore only I fortune sphere. But without a long and painful battle, and no need to have an elite party.

Obviously I would not generally recommend this approach because it makes the whole monster arena pointless. But to get the extremely rare and important fortune spheres surely it makes sense. Why knock yourself out?