"At full quality in overwatch, I can get around 120 fps solid. " ... to quote an old but still funny TV commercial ... "where's the beef ?" What is the purpose for the upgrade ?
a) To take advantage from the improved performance between 120 and 144 hz
b) To be able to tell ya friends, you play at 144 hz.
Been there, tested that. Turn ya GFX settings down as you described so you are at 144 hz or above. Than go into monitor settings and change refressh rate to 120 Hz. We've done that without telling 5 users and none of them noticed. And yes, after a week, we asked if they'd notice if we did this ? 4 said yes, 1 "I dunno" ....
So unless it's b), sit tight. You have plenty of life left in the system.
It's a simple thing to see if your GPU is bottlenecking... Open Task Manager... Look at the performance tab and run the game for 10 minutes, is the graph pegged (100%) ? Hit the resources button, select resource monitor, CPU tab and try again. Is it pegged ?
I didn't see any specifics about your monitor ... is it G-Sync ? Is it capable of ULMB. Almost every G-Sync monitor is capable of switching from G-Sync to ULMB. In addition, non G-Sync monitors like the Asus VG248QE for example can be used with motion bur technology via the toastystrobelight utility. If this is an option for you, would strongly advise you to use ULMB or Toastystrobelight (TS) at these frame rates. My son was playing on a 165 Hz monitor (XB271HU) for over a year before he tried ULMB and when he did, he just sat there playing with his mouth open for 10 minutes.
If ya have G-Sync, use the settings to turn off G-Sync and try ULMB ... if ya one one of the monitors listed under Classic Lightboost Blur reduction" on the link below, try the TS utility
https://www.blurbusters.com/faq/120hz-monitors/
As for a upgrade from your 980 Ti to 1080, to my eyes it's too small of an upgrade to bother with at 29%. Yes, ya system is a few years old but I can't see upgrading at least until the next CPU / GPU generation drops (or one after that) and ya do a complete new build. This month or next we will see new monitors from Asus and Acer w/ the new 144 Hz 4k HDR Panels from AU Optronics. These will start from $1699 to $1999 but the one effect they will have is the cost of the 165 Hz , IPS ,monitors with the 1440p AU Optonics panels will drop yet again.... even now they can be had for $499.
If ya gonna do an upgrade, might as well include a jump in resolution and monitor type as these mionitors have dropped well into the affordability range.