First, your rod tip should always be up, 45% angle at minimum, for two reasons: 1) it helps to keep the line off the water, minimizing drag, and 2) the rod is able to bend when you get a fish, giving you some chance to turn it before your tippet pops.

Second, people with much more experience fighting big fish than I have suggest to fight the fish with the rod to the side, putting sideways pressure on the fish rather than straight up. With sideways pressure, you may be able to guide the fish into quiet water, with the rod straight up you have no control over its direction.

It may be that where you were fishing on the Madison the current was stronger than where Vinny was on the San Juan. I've never fished the San Juan, and never caught any really big fish on the Madison.