I’m sorry to hear about your trouble, and I’m also sorry to tell you that permanently removing warps in solid wood furniture parts is virtually impossible after the fact. If the warp is large enough to be an issue, then it’s too much to get rid of now. The only option is to build yet another top so it won’t warp, then install it in a way that prevents splitting. Unfortunately, the woodworking knowledge required to make this happen is becoming scarce.
Wood warps in response to the loss of moisture and to the nature of grain structure. The trick is to let the wood do all the warping it’s going to do ahead of time – before you start making the top – then mill the warp out as part of the construction process. Your new top was probably built with wood that was just a little too wet. This is very common. And if the grain of this wood was also wavy, or had knots, then warping would be worse. Even lumber stored in an unheated space for decades will never get dry enough for trouble-free furniture. Seasoned wood needs to spend several weeks in a fully heated space before construction if the finished product is to behave properly.
One reason your original top split was because your dry sink was made before the time of central heating. Back then, homes remained cool all winter, causing wood to dry out much less than it does now. The seasonal change from humid summers to fully heated winters that we experience these days makes wood expand and contract a lot more seasonally than it ever used to, even if it was properly dried before building. That’s why your new dry sink top needs to be mounted in a way that allows seasonal movement. One option involves the use of metal Z-shaped clips. They hold the top down firmly, yet allow it to expand across the grain without the kind of restrictions that cause cracking.