The "strong chlorine smell" is not a good thing. A clean pool will have almost no chlorine smell even with a high FC level. I maintain a CYA of 40 with FC of 7-9ppm in my pool and it has almost no chlorine smell at all.
That strong smell is due to combined chlorine (chloramines), spent chlorine that has been consumed by killing algae but has not burned away and remains in the water. It's a normal process that happens, but you have lots of algae to kill so your chlorine is quickly consumed and converted to combined chlorine. Even though it is still in the water it is not capable of doing any more killing. This is where the shock process comes in, you elevate chlorine to high levels to burn away the combined chlorine.
A quick up and down of high FC does not do much when you have algae, you need to SLAM.
Shock Level And Maintain, that means elevate the FC to shock level and hold it there so it can kill all the algae and burn off all that combined chlorine that will be produced in the process. If your CYA is 35, then call it 40, your
"shock level" is 16 ppm FC. You would need to get FC up to 16 and keep it there by frequent testing and dosing with bleach. The chlorine will rapidly be consumed at first so you must test a few times per hour in the beginning. As the algae is killed off the chlorine will hold for longer periods and you will be able to cut back on testing/dosing. Very important that you don't let the FC level fall even for a short time, as soon as the killing stops the growing starts.
This is where the FAS/DPD test is important. It can accurately test these high levels of 16ppm or even higher, and it can also test for the presence of combined chlorine. It is a "must have" to do the process and most every other kit out there does not provide it.
You definitely want to stick with liquid chlorine, you can use "liquid pool shock", "chlorinating liquid" or plain old bleach these are all the same thing sodium hypochlorite. The pool shock is a higher concentration at about 12.5% where bleach is only 8.25%, exactly the same thing, you just have to add a bit more to do the same thing.
Dry chlorine shock or tablets add CYA to the pool with every dose. This will make cleaning it up even harder so you want to avoid those. It's very important to this process to know exactly what your CYA level is. Higher CYA will take much higher FC to do the job. All those bags of shock you added typically raise CYA to the point this process can't work. Often people come here with CYA levels well over 100, the only way to reduce CYA is to do a water change.