Before you go the blow torch route, let's see if maybe you can just fix it by replacing the cap. If not, you can still try to replace the valve.
Look at my video above about replacing the R528 cap. No need to go buy one right now. You already have a new one in your 528MP (assuming that the valve in your toilet looks like the valve you just bought, at least generally -- it can have a different color (like blue) cap, and won't likely have the little adjuster, but if it looks the same, then you can try the swapping the cap method. On the video, you will see how to remove the cover, remove the float, unscrew the cap. You can do that on both valves and swap out the cap. Also try cleaning the strainer in the old valve, which pulls right out like shown in the video. When you reassemble, see if that solves your problem, and reset the old valve to the proper height (with the fill line about 3/4 inch below the top of the overflow riser). Don't worry, that's not a precision adjustment; if it's 1/2" it's fine.
If that fixes the problem, then we're all set, and you can put away the hammer, chisel and blowtorch for now. If not, then we'll have to come up with a plan B, and a photo of the toilet and the area you're talking about having problems with would be helpful.