actually P3680 board looks just like XPS 8960 or Aurora R15.  all have 12 + 4 +4 socket on mobo and use same line of psu's.  Dell does this all the time.  almost same oem board with slightly different minor detail and different bios put in different case and call it a different model.

you will get your answer by looking at XPS or Aurora users connect 1000w psu to Dell RTX 4090 oem

https://www.reddit.com/r/Alienware/comments/10lhqmx/aurora_r15_13600kf_rtx4090_review/

https://www.reddit.com/media?url=https%3A%2F%2Fpreview.redd.it%2Fa-big-problem-with-dell-xps-8960-and-pci-slots-v0-gja4jgbfes2c1.jpg%3Fwidth%3D3024%26format%3Dpjpg%26auto%3Dwebp%26s%3Ddb805531cd06e38e6d2323306a86e7927e6a0541

OP you are correct an angled adapter is needed as show better in 2nd pic.  if you zoom in the reddit webp pic you may see the cable DP/N is Y35RH

from R15 spec model it is 

R15 has three kinds of Dell DGPM for various gpu.  all these apply to Precision too

Many of retail cards will also provide 12vhpwr angled adapter with the cards.  If your does not come with one, it can be source from big shopping site.

You may concern about power supply does not provide three 8-pin cables for graphics.  On the older workstations Dell uses one 8-pin to dual 8-pin dongle, with Dell part number 0G22MM, to provide up to four 8-pin PCIe power cables for graphics.

Thank you all for the replies. I will certainly source the 3x8-pin -> 12vhpwr angled cable, from Dell or elsewhere.

As some of you speculated, the remaining issue is the power ports that the Power Supply provides. Right now, what's available is 2x8-pin, plus 2x6-pin. Should I get a 2x6pin -> 8-pin adapter to create the 3rd 8-pin input? Or a splitter as suggested in other postings to split one of the provided 8-pins into two? What do you see in your other Dell systems that use a 1000W Power Supply?

Thanks!

this says 2x8 pin from psu but the pic shows three cables coming out of it.  I speculate the 3rd cable just connect to 2x6 pin from psu combined into a single 8 pin.

Just to follow up on a solution that appears to work (for me at least). 

I used a 2x6-pin to 8-pin cable to create a 3rd 8-pin input, and then an angled 3x8-pin -> 12vhpwr adapter to plug into the 4090 itself. This seems to have worked! It's a snug fit, but apparently it's working. 

For reference, when I tried to plug in *only* the 2x8pin inputs into the GPU, it would not power up.

Thanks for all the advice!