CPU and Cooling upgrade options for my Precision T3610

I have a Dell Precision T3610.

It has a Intel Xeon 1620 v2 CPU. I tried looking up information on what CPUs it supports and found this:
.

Which states that I can't really go higher than a 1650 v2 at most.

However on Dell's forums I see people saying they were successfully able to install up to a 2697 v2:
https://www.dell.com/community/Precision-Fixed-Workstations/Dell-Precision-T3610-Processor-Upgrade/td-p/7712266

And other upgrade guides that state it maxes out at a 2687 v2:
greenpcgamers.forumbee.com/t/634f91/precision-t3610-hardware-upgrade-guide

So I have no idea if the 1650 v2 is just an officially sold configuration but the motherboard can actually handle much better, or if that's a completely different system than mine and I am mis-understanding. Also from my understanding if I go that route since those are 150 watt TDP cpus, higher than the 130 TDP one I currently have, I would need a better cooler and I have no idea what kind of 3rd party cooler would even fit in this proprietary Dell case other than a Noctua NH-U9DX i4. 

 Looking at all my options, and the costs, seems like the "sweet spot" would be the E5-2667 v2. First of all, I wanted to know if this CPU would even work with my system or if anyone here has attempted this same upgrade. And after that, I also wanted to know if I would have to replace the cooler it comes with. The current CPU I have now and the 2667 v2 are both listed as having a TDP of 130 watt, so I am hoping the existing cooler would suffice if possible, or if the 2667 v2 still runs significantly hotter than the 1620 v2.