Jack already accomplished part of his objective when the minks failed in their own
His objective wasn't to allow anyone touch Kaido
With him knowing of the Sulong timespan
On the other hand, the sulong minks(including Musketeers and guardians) wanted for the scabbards to conserve their strength
Yet, he already bodied the army including top musketeers / guardians pushing Inuarashi / Nekomamushi to transform into Sulong and intervene
And as mentioned, Jack already pointed out the Sulong timespan before
So i think Sulong Neko / Inu will start dominate, but most likely Jack's awakening will allow him to stall for him long enough to recover and after it potentially turning into a hybrid Jack vs post Sulong Inuarashi / Nekomamushi