Shocks have nothing to do with ride height, especially on the front. (air shocks are a different animal, they combine the shock with an air bladder that can adjust ride height a few inches, also struts can be used to change ride height, but that would require even more money). Shocks are dampeners, meaning they control the rate of a spring’s reaction to compression/extension by absorbing some of the energy and turning it into heat. If you live on the east coast, there are people that understand weight jacks, that might be something to look into.
As mentioned above, your cheapest route is stronger springs, another is to get tires with different aspect ratio…the newer, low profile 225 x 40 vs. older F60 or F70 wide ovals or regular passenger car tires (with 78 or 80 aspect) may have 2 inch or more difference in total height. Also moving from 14 or 15 wheels, up to 16, 17 inch, with the appropriate tire, can also raise the ride height of the car.
A lot of class racers swear by having tall wheels/tires on the front for better roll out, reaction times. Not much for comfort or handling, great for drag racing.
The point is shocks are not going to solve your problem. The best they can do is slow down how the wheel reacts to a bump or pothole. The cure for distance between headers and speed bumps is to raise the car.
What may help is how you go over speed bumps. Hitting them straight on is not the way to do it. If you go over them at an angle, sometimes thats enough to widen the amount of time one wheel or the other is on top of the bump, which allows the car to ride a little high ove the bump.