https://opencores.org/
Its a RISC core and its open hardware.
As with the Geode platform, the HW may be actually decent, but the full software ecosystem is all that matters. Going for something that is off-mainstream means a lot of extra development and later during the product lifetime, a lot of hard work to keep it going as the others may be dropping of their input on the platform. So unless you're just playing around, inventing the wheel is not commercially viable. Stick with one of the large SoC vendors work; even if they deprecate the part and do not keep current the OS support, there are a lot of folks like you and everyone can benefit from eachother. I've worked with plenty of old ARM chips, that are still supported with new kernels as there is demand for it, although the chips themselves are not used in new designs for ages.
In addition, the FPGA based soft-core stuff can not compete price-wise (bang for buck) with hard asic-s, that's why the FPGA vendors are adding their hard CPU IPs in there (ie Zynq).
As I understand the original poster, he needs a well-supported linux-running board to plug his PCI card into. Starting from scratch and designing your own hw usually breaks the budget unless your quantities are very large.
As for the imx6/7/8, afaik they have only pcie, not old pci. Finding and existing board with pci interface is not very probable. Of the new ARM Cortex-A SoC-s, the imx is one of my favourites at this time and considering the complexity of the chip, the amount of issues has been reasonably low.