Chrono Cross to recharge elements once
If you think that the Plates would help somehow, then Crono's Techs (or his own set of Elements) would certainly disrupt the Elemental Field...so the Chrono Cross would be a waste of time...
Because like I've said before...Any Element Serge can equip, Crono can...and probably better...! 
The obvious exception being the Chrono Cross itself - and the
entire purpose of it here is a one-shot "recharge all elements" (though, obviously, with the Recharges, he's getting it back repeatedly until he runs out - this gives him ~30 uses of everything he's got). It then becomes a battle of attrition - can Serge run Crono out of MP
and Elements before Serge runs out of Elements to use? Serge has the (dubious, and only potential) advantage of summons, obviously - since we can't even agree on what innate Crono would be under the CC system, it's entirely possible that he can't use
any of them because his innate doesn't directly match any of the existing ones (in which case the Plates are definitely useless, and we can either resort to the Ghetz's Shirt + 3x Winged Shoes for Evade +104% strategy [assuming Serge managed to find the Shirt hiding under a Gameshark, ha ha] or a Prism Vest).
If Crono's got a known innate, we have a 50-50 chance of being correct on it and thereby making the battle extremely long (especially if Crono is
also innate White - at that point, it's basically "Serge resorts to an Imbecile/Genius/off-color element/CC or Recharge cycle" if not an outright draw) or being wrong and thereby requiring some manner of re-using high-powered healing Elements (HolyHealing, Saints, etc.). Since if he's
wrong, the worst case is Yellow Plate vs. White Crono (Saints is effectively useless other than for healing purposes and may just be a "reset battle" button in the absolute worst case), Serge has no reason to use anything other than a White Plate (mostly useless against Yellow Crono, moderately helpful against White Crono, and against "Canary" Crono... about the same as Yellow Crono). TurnWhite is always an option to force Crono's physical attacks to heal you in this case, though again, Serge would need to be able to change it repeatedly.
The Turn<color> Elements are useless to Crono except for the purpose of removing TurnWhite.
The other effect of the Chrono Cross, which
is based on the element order, is entirely irrelevant to this fight, unless you're trying to imply that Crono is himself the Time Devourer.

Really, it looks like more likely than not it'd end in a draw (read: they get bored after an extremely long time of not really doing anything in the way of damage that lasts more than 3-4 rounds).
So, ideal setups for Serge to at least force a draw:
Mastermune in all setups
Elements: Imbecile, Numble, Nimble, BatEye, HiRes, MagNegate, assorted healing (including Saints), lots of Recharges, Chrono Cross, possibly Unicorn solely for MDef boosting
Evasion Setup: Ghetz's Shirt, 3x Winged Shoes; replace Nimble and BatEye with additional healing
Element-Using Setup: White Plate, Moonglasses, 2x Winged Shoes; add assorted attack elements and TurnWhite
Full Attack Setup: White Plate, Sunglasses, 2x Dragoon's Glory; add Strengthen, LoRes, EagleEye, TurnWhite