Catches don't diminish with speed, rather with tool control. You've got three good helpers to give you control - the rest, your arm and the work itself.
The rest should be kept in close, as close as you can manage, and if that means stopping and adjusting closer every minute, so be it. Idea is to limit the downward distance the tool can move in a "catch."
With the rest in close, and your "good" hand out near the end of your tool handle, you can make large moves at the handle which make small adjustments at the cutting edge. You also have, if you keep the tool handle within a 20 degree angle to horizontal, a great force multiplier to counter downward thrust as well. This multiplier (leverage) diminishes as the tool handle falls. At 90 degrees your arm and the work are on an equal footing or less, since you have to support the weight of the tool as well. Makes your rest pretty well worthless as a support as well, so you're in double jeopardy.
The work also helps with tool control. You can keep the tool at an effective angle more easily if you let the bevel of the tool maintain contact with the wood where you've been as you move toward your destination. Lots of grinds have variable angles, which can make things unstable and cause the tool to roll and catch, since they have a gap behind the bevel along your direction of advance. So stay in the sweet spot and don't make pitch or roll adjustments that might get you in trouble. Yaw the tool into (and out of) the work.
The wood will teach you how it wishes to be cut. When it's willing, the shavings slide down or across the tool with almost no pressure on your hand. If you increase depth of cut you increase the pressure downward against the rest, which doesn't care, and against your arm, which may tire, but so long as you're on both rest and bevel, you won't catch.