R7450 Wake on Internet

   Again, bear in mind how much I know abou WoL, ...

> [...] but the router 'forgets' the PC's IP a few minutes after power
> off. (i.e. WOL is useless after that tiny window after shutdown). [...]

   There are two addresses of interest for this stuff: the IP address
and the MAC address.  Port forwarding (and, I assume, your VPN) works at
the IP-address level.  WoL works at the MAC-address level.  The router
might remember the IP address longer than you think (DHCP lease time =
1 day?), but the IP-MAC association might evaporate much sooner.  The
connection between the two is ARP:

      https://en.wikipedia.org/wiki/Address_Resolution_Protocol

And ARP relies on link-layer broadcast messages (MAC address
"FF:FF:FF:FF:FF:FF") which is the kind of thing which I might expect to
get blocked by an IP-level transport like, say, a VPN.

   That's why having a gizmo like a Raspberry Pi on the LAN is
advantageous for something like remote WoL.  You can talk to it at a
high (routable) level (SSH, say), and it can shout at its immediate
neighbors using low-level (link-layer) broadcast messages.

   Port forwarding in a router (or use of a VPN?) can get a message
addressed to the destination LAN IP address, but, unless the router can
translate that IP address into a (local) MAC address, that's the end of
the line.  Which may be why that third article talks about stuffing the
router's ARP cache with an artificial (permanent?) ARP entry.

   But "permanent" is a relative thing, and you'd need to do that every
time the router starts, unless you can find a way to jam those data into
the non-volatile firmware storage.

   As for Telnet access to your router, which might let you do any of
that, I wouldn't depend on it.  Netgear appears to have been removing
that (undocumented, unsupported) feature from various models in recent
times.  Whether that's intentional or just another blunder is not
obvious.  See, for example (different model):

      https://community.netgear.com/t5/x/x/m-p/1786837

   You can try it, but I wouldn't be amazed by a failure, and, even if
it works today, the next firmware version could break it.

   Everything's complicated.