Going way back, there was once a service from ????? to Waterloo. It was to connect with Eurostar and used the NLL to get around London. I'm seem to recall that this service stopped at Finsbury Park. May have been before GNER.
I recall vague details of that service.
Didn't it start from Edinburgh, and called at certain East Coast stations to pick-up only, and, as you say, went round the North London line to Waterloo to connect with the Eurostar services?
But I can't remember if it called at Finsbury Park, and never managed a trip on it because it was limited to Eurostar ticket-holders only.
Going further back into the 1970s, Finsbury Park was regularly used by a "budget-price" train to Newcastle called "The Highwayman". It was intended to compete price-wise with motorway coaches, and took about 6 hours to get from Finsbury Park to Newcastle. It must have been routed on the slow lines wherever they existed and visited most loops on the two-tracked sections!
IIRC, it left Finsbury Park about 10am, and presumably used that station to begin/terminate its journey because of lack of platform availability at Kings Cross. Or perhaps the then Eastern Region did not want such a train, composed of Mk 1 coaches and a Cl.40 at the head to sully the image of prestigious high-speed trains at The Cross!
I seem to remember it lasted only for a couple of seasons or so!