The cheapest way to extend an already existing Travelcard is a Boundary Zone 6 - Gatwick Airport
CDR, priced at £4.10 with your Railcard.
This is routed "any permitted" though in practice there is only one geographical route (with the option to go via Redhill station on the slow lines, or avoiding it on the fast lines) and one train operating company (with the option of taking any of their route brands running on the route at the time).
While not answering your question, for the benefit of anyone stumbling across this thread and wanting a literal answer to the question in the title, assuming no pre-existing ticket is held, the cheapest way to do a single journey on the company's Gatwick Express route brand, from Victoria to Gatwick, is to wait until any of their trains is scheduled to depart from any platform other than platforms 13 & 14 and use contactless or Oyster PAYG, at off peak times this costs £8 (undiscounted).
By the way, the cheapest way to "experience the 442s" for a Zones 1-6 Travelcard holder is to simply travel between Victoria & East Croydon. I mostly tend to make this journey late evenings, around 2230-2300 and nearly always the train is booked to be a 442. Though this may not last for much longer. There's also at least one evening peak departure from London Bridge (to Eastbourne) which is booked 442.