I did some very thorough chassis investigation. (I have no prior knowledge of the stuff so i'm learning it all at once.) When the car had the chassis done, the engine and trans, interior, etc were not in it. The 4 link was just set at a base random setting. We've always tinkered with shock settings and spring settings and tire pressures. Others have offered advice on pinion angles and how to set the rear shocks/springs and even how to set the 4 link. None seemed to help. I read everything I could from chassis companies online and other general math/geometry equations on how to figure this stuff all out. What did I find out? The car was nowhere close to being right.
The car is porpoising. This will happen when the front and rear springs have a frequency that is close to each other. Imagine a teeter toter with a spring under each end. Just as weight is making one side fall, the compressed spring on the other end is pushing up. When the other side comes down, the process repeats itself and the energy keeps switching from end to end back and forth. The answer is to put lighter springs in one end of the car. Or stiffer. An instant center that is directly under the center of gravity can also produce the affect (or is it effect. I forget) or exaggerate the previous condition with the springs. Also, is the front of the car limited?? looks like it could use more travel. The car doesn't have enough hp to produce the desired weight transfer by sheer acceleration alone. It needs a little help. Also, run tubes if you don't have them already. Or better yet, a stiff sidewall tire. Unfortunately, nobody I am aware of makes them in a 9" tire.
Thank you for all the potential suggestions. I checked into your ideas. Front springs are 450, rears are 200. They aren't close enough to bounce back and forth with each other thankfully. The instant center? No where near the center of gravity. Is the front end limited? Yes, by the stock snubbers on both control arms to prevent bottoming either way. I do not think now that this has as much of an effect as the 4 link did, but pending future results it could be the next place to check. The tires do have tubes, and we run the D05 stick compound Hoosier tire that all the high flying NHRA Super Stocks do.
Cool videos!
The car looks and sounds great!
I'm no expert but if you have an adjustable four link I think raising the front of your lower bars one hole might help you hook a bit better. If you watch the second video closely, it looks like the back end of the car squats just a bit when you dump the clutch. (looking at the tire in the wheel well) Raising the front of the lower bars a bit will move your instant center up a bit which should cause the tires to plant themselves harder when you dump the clutch. At least that's the way it's supposed to work.
It's hard to get a good baseline suggestion for a four link because the best setting depends on how much power the car has, how heavy it is, wheelbase, standard or automatic etc. but they do say that setting the suspension so that the back end squats a bit is usually not the best way to go on a ten or eleven second car. I gather that you usually don't want squat, either a neutral setting or if anything a little bit of lift on the rear end is usually best.
Your idea brought me to investigate this and instead of relying on others, teach myself how it works and how it should be set. I can't thank you enough for the observations. I finally was able to get to the car and measure and calculate everything. I learned about how to check the center of gravity, the percentage of antisquat, the instant center, and the percentage of rise. As you were saying about the setup needing to be neutral or even a little lift, neutral would be a 100% antisquat rating. I'm sure you know, and from what I have learned, anything above is planting the tire and lifting the rear, anything below is squatting the rear and pushing the tire up. The results? The car had an antisquat of 46.86%! The instant center was nowhere close to where it needed to be, it was very low and very forward. After recalculating the angles and measures, I moved the bars accordingly, and recalculated and measured again. The results? The car now has an antisquat of 100.08%. The instant center is right on the neutral line and about 10" forward of the center of gravity, so it should hopefully still pull the front wheels a little.
I can not wait to get to the track and see what the results yield. It's all a big learning process and we certainly appreciate the insight. You guys are great!
Finally on the 4th run when I was shifting from 3rd to 4th just before pulling the shifter I saw the light blink on. Thought.. "Huh there it is.. timed that pretty well" And saw it on through the finish line. By the 6th pass I was able to pay attention to the tach just as the tree started to come down and the shift light and glance at the tach going through the lights. I definitely feel much more comfortable in the car. After the initial shock of "don't miss a shift, don't forget the clutch, don't crash the car, don't blow the engine." It actually gets fun! 
I'm unsure about Cordova next saturday. That's a long haul for us. We're probably just going to keep it local for the balance of the season. I appreciate the offer though!
(I hate it when actual results don't fall in line with our super smart theories) 