In case you are curious, I did it as per your advice. Two PSUs with add2psu, and a large case specifically engineered for supporting them. Also posting it here for someone else who seeks to build a multi-gpu rig with appropriate lanes and power.
The good thing is that all this contraption was not expensive (100 euros the case, 67 euros the second psu, 6 euros the add2psu).
The xeon-e5v2 workstation has been bought crap cheap from ebay.
The only expensive things were the GPUs (1080ti + 1070), for a total of almost 1200 euros. I’ll add an NVMe drive soon, and a little one slot video card to leave the two GPUs alone for DL.