The pushrod 4.0 doesn't make much more horsepower than the 2.9: 10-20hp depending on the year and vehicle. In a race it's horsepower that matters, regardless of what rpm, and the 4.0 isn't making that much more. In regular use, the 4.0 is much, much better than the 2.9 because it makes a lot more torque--more horsepower at lower rpms where you use it a lot. If your truck is geared for that engine to be hitting its maximum rpms then there is no advantage to swapping in a 4.0. If you were trail riding or rockcrawling or towing a trailer or just driving around, the 4.0 is a lot better. You are racing and keeping the engine near its maximum rpms and getting your torque from gears.
The only real problem with the 2.9 is the speed density system. Swap to a MAF meter system and then whatever you do to improve airflow through the engine will make a difference. What you want is to move more air through it and use that air to burn more fuel and make more power. You want rpms, and lots of them. Spinning that engine at 6,000rpm will make 180hp, if you can get it to breath. You would have the same breathing issues with a 4.0 if you swapped that in. The 4.0 is bigger and could theoretically make more power, but it's the same route with either engine. Where are you going to get the parts? Who has flow-tested port work on these and will do your heads? Who can make an intake manifold to replace the truck-tuned one Ford put on?
Doing what you are doing, I'd work with the 2.9. Racing is partly seeing what you can get something to do. Why not use what you have?