I've assembled the board and it's working!
I did gain a couple of gray hairs though during assembly - once I reflowed the board, +5V input power rail was shorted to ground!
I traced the problem to the PMIC chip since some other pins were also shorted. After several attempts to resolder pads without removing the chip, I've concluded that the problem is with the chip itself, so I needed to replace it. This was a moment I regretted using lead-free paste as removing the chip (it's QFN-48) was quite a chore since my board had two full internal ground planes and so could take A LOT of heat - and I didn't have preheater (now it's on my shopping list). Once I took it out, I decided to use regular leaded solder for a new IC. That was much easier and faster of course.
After that I've accidentally applied power backwards for few seconds until I realized that
. Once I reversed the power, only two out of 4 rails came online. Fearing for the worst (that I blew that chip too), I decided to touch up all QFN pins once again with an iron and see if that helps. And IT DID! All power rails came online and I saw "power good" LED came on.
Once the power issue is resolved, I've verified that Vref on JTAG connector is what it should be (to make sure I won't blow up the programmer) I connected programmer and plugged it all to computer. And Vivado recognized the chip!!!
There are two interesting things about this board. First of all, it included a single 512 MBytes (256Mx16) DDR3L chip, which has its "chip select" line permanently grounded as otherwise there are not enough pins in a single IO bank for ADDR/CTRL lines. I've quickly built a test design with DDR3 controller and Microblaze CPU to confirm that memory works, and indeed it did work! Second interesting thing is using 1.8V QSPI flash IC - I wanted to check if it's possible in principle to build a system without 3.3 V rail at all to save on DC-DC converters. And it turned out that it's entirely possible, so that if all your peripheral chips can work at 1.8 V, you can get rid of an extra DC-DC for 3.3V rail. There are a couple of gotchas though, so if you want to build such system - make sure you use schematic checklist spreadsheet provided by Xilinx to verify all your connections! I do have 3.3V rail on this board as I use it for HDMI stuff, and there is an option to set IO voltage for one of extension connectors, but both banks 0 and 14 (where configuration-related pins are) are completely devoid of anything 3.3V.
Finally, this is the first more-or-less complex board of mine that actually works on a first revision!
In case anyone's curious, here is a schematic of this board:
https://1drv.ms/b/s!AkGeV4xlumxjg84U2EyEBlXt-h4mQQ