In additional to the usual countercurrent configuration for minimal heat loss and the cocurrent configuration occasionally used, a recuperator-type heat exchanger may be arranged in a cross-current configuration for process intensification, where you have alternating layers of pipes in the X and Y directions. (A rete mirabile is a much better way to do high-density heat exchange, but that is a different topic.)
This cross-current configuration is optimal, however, for a different purpose: rapid zone melting. Although I suspect that the speed of zone melting is limited by crystal growth speeds, maybe you can still do it faster by doing it in thin pipes (made of a material that doesn’t dissolve significantly in the material you’re trying to purify, of course). You can run hot coolant through only one or two cross-current pipes above and below the layer of the material being purified to melt it in a narrow region, while perhaps simultaneously running cool coolant through other adjacent pipes to intensify the temperature gradient.
By switching between pipes, it should be possible to rapidly move the molten zone along the material being purified.