Try searching the DigiTrad. I can't clarify lyrics on your recording, but in the version I learnt (Vaughn-Williams) it's Ramehead, rather than Ramhead; & Dodman, not Deadman or Deadland. Both of those are on modern maps too (Ramehead being just outside Plymouth, Dodman Point is more or less due South of St Austell). I've never heard/seen Dungeness for Dover (except in the DT version). It's plausible in geographical terms, Dungeness coming before Dover if you're heading East up the Channel, but rather spoils the scan of the song.

And if anyone is wondering, Fairlight is just East of Hastings, South Foreland Light is actually an NT property nowadays, a little East of Dover (North Foreland is about equidistant, following the coast, between Ramsgate & Margate), & The Downs (presuming there wasn't more than one) lie just off of Deal.

The V-W version of the fourth verse is:

Then the signal was made for the Grand Fleet to anchor,
And all in the Downs that night for to lie,
Let go your shank-painters, let go your cat stoppers,
Haul up your clew garnets, let tacks and sheets fly!