Threadripper is actually not even that great here, it's NUMA (half of the lanes are attached to each die) and if you just want NUMA you can do a dual-socket E5-2650 system for like half the price. Same logic applies to TR here:
https://www.servethehome.com/how-intel-skylake-sp-changes-im...
You're not using the CPU for anything, there is no reason to have a beefy 12-core CPU there. If you really want Threadripper, the 8-core version is fine.
Again, personally I'd look at X79 boards, since they are pretty cheap and you can do up to 4 GPUs off a single root, depending on the board. There are new-production boards available from China on eBay, see ex: "Runing X79Z". Figure about $150 for the mobo, about $100 for the processor, and then you can stack in up to 128 GB of RAM, including ECC RDIMMs, which runs about $50 per 16 GB.
There are some Z170/Z270 boards like the "Supercarrier" from Asrock that include PLX chips to multiplex your x16 lanes up to 4 16x slots (does not increase bandwidth, just allows more GPUs to share it at full speed!). They also will not support ECC (you need a C-series chipset for that, which run >$200). So far most OEMs have been avoiding putting out high-end boards for Z370 because they know Z390 is right around the corner so there is currently no SuperCarrier available for the 8000 series.