If Gavilar managed to swear an Oath, which I doubt, because the Stormfather said no one had bonded him in a long time, then he would have probably made it to where Dalinar is now.
As to how he interpreted the visions as needing to restart the Desolation cycle, Gavilar...had an odd thought process. He tried to be too subtle with it, searching for a meaning that wasn't there and overlooking what the purpose was, and with all of the visions focusing around the Desolations and their effects, he thought that meant he needed to prepare to not have everything destroyed by forcing a Desolation along because the humans never started (that the visions would have let him know about), and thus were always on the offbeat from the very beginning. He wanted to reverse that and perhaps end it forever with an unequivocal victory for his side.