A lot of odd replies in this thread, but hey, it's MacRumors...
For no cost, OP could try turning on the built in Screen Sharing on the new Mac and the open the Screen Sharing app on the old iMac and connecting to the new Mac.
Performance is at least decent, and yes I use it all the time so this isn't some sort of hypothetical answer.
To improve the performance even further, the new Mac and the iMac could be connected via Thunderbolt and then networking between just those two Macs could then be set up, giving a very high speed & dedicated connection between the two.
The old iMac would only have the thunderbolt connected and no other networking connection active. The new Mac would have both the Ethernet (or Wifi) for LAN and WAN access turned on, plus the thunderbolt connection active for the screen sharing. You wouldn't turn on Internet sharing for this.
I've also done this thunderbolt networking, it works fine, great even.
Now, whether this is up to what the OP wants in performance is their call. But it's easily done so they can see if it works for them.
Is it perfect? No. But it's worth the time to quickly check it out.