I ended up using Screen Sharing (via Tailscale + VNC in my case because the machine is remote) and dragged an updated version over to the 10.13.6 machine. The tricky part is that as soon as you quit Tailscale you’ll lose the screen sharing connection. Hence a VNC to access the machine outside of Tailscale and do the update. ARD is way expensive so I use Edovia’s Screens 4 which is a bit quirky but does the trick once you get used to it.
I’m not sure what you mean here but you were obviously able to download the updated version so the above approach might help.