I have a P6T Deluxe and it's not specced to run on that either....but I've heard Xeons can sometimes run in place on certain boards.....even when not on the list.....but I wouldn't know with these boards specifically.
If you're gaming on this old platform it's going to suffer a bit. I had a i7 920 in my Gigabyte U3DR mobo and installed a 960 with a mild overclock to 3.8GHz. This didn't help with micro-stutters in some games such as BF V when using a RTX 2070S.
That was my first real gaming PC and it's still running today. The biggest upgrade to improve performance was an SSD. But it's been retired from gaming.
The Xeon W3670 is a good processor for X58 motherboards. They sell for only $25 on eBay.
The Xeon W3680 is exactly the same as the Core i7-980X but the Xeon always costs less. Both have an unlocked multiplier so they are easy to overclock on any X58 motherboard. The Xeon W3690 and i7-990X are the same CPU. All of these overclock to more or less the same speed so no need to spend extra money on a more expensive processor.
Generally ebay is your best bet for sourcing CPUs of this era, although AliExpress can also be useful.
The Xeons are often much better value than the i7s. I recently got a Xeon X5670 for all of $10. Out of the box it's a bit slower than the i7 980x/990x, but I was able to overclock it to ~4.3ghz (via bclk) which would make it outperform a 980x/990x for a small fraction of the cost.
I cannot say for certain, but I would be very surprised if your motherboard did not work with Xeons. Most X58 boards can accept Xeons even if the board doesn't specifically list support for it.
For example, I use the X5670 on an MSI X58A-GD65, which doesn't officially support any Xeon X series chips. My Asus Rampage iii Formula doesn't have support for any Xeons officially, but has worked with both the x5670 and e5620 I have tried.