It's probably hard to code system wise to make the Wyvern vanish, then reappear.
I still say Spirit Surge should reset the Call Wyvern timer. Or, let use use Spirit Surge even without a Wyvern, but when doing so, call our Wyvern with a "Rouse Wyvern" state. Rouse Wyvern was our old SP2 which made the Wyvern unkillable for 45seconds and gave it shortened Breath JA timers and increase attack/haste/accuracy. This would allow DRG to use Spirit Surge differently depending on the situation.