You can use Oyster all the way to Gatwick. It's cheaper than splitting at Farringdon; the fare would be
£14.30 with your Senior Railcard applied. However, a 'Thameslink only' Off-Peak Day Travelcard is cheaper at
£13.70. If you were travelling on a weekend or Bank Holiday then the Super Off-Peak Day Travelcard would be available, costing only
£12.55.
The through paper fares aren't worthwhile buying, like you say. They're priced based on their validity on the Gatwick Express, which is charged at a premium despite the poor service it offers (only half hourly!).
If you do want to use Oyster, it's cheaper to 'split' with Oyster at East Croydon - ie. leave the train, touch out at the barriers and touch straight back in). Trains from East Croydon run every few minutes so it won't take you much longer. That would cost £10.00 + £2.70 =
£12.70, assuming each section of the journey was begun at off-peak times (i.e. not Mon-Fri 06:30-09:30 or 16:00-19:00).
There are even cheaper options. In increasing order of cost, and assuming off-peak travel:
- Taking the SL7 Superloop bus to Croydon and then the train: £1.75 (or free with ENCTS pass) + £2.70 = £4.45
- Taking the Piccadilly line from Heathrow to Earls Court, the District line to West Brompton, the Overground to Clapham Junction and finally the Southern train to Gatwick. The through PAYG fare is £6.95, splitting at East Croydon reduces it to £2.55 + £2.70 = £5.25.
- Taking the Piccadilly line from Heathrow and then the District line to Victoria: £4.65 to East Croydon + £2.70 = £7.35. Splitting additionally at Hatton Cross reduces that slightly: £0.00 to Hatton Cross (it's in the free Heathrow travel area) + £4.15 to East Croydon + £2.70 = £6.85
- Taking the Elizabeth line but avoiding Zone 1 by changing at Ealing Broadway, Shepherd's Bush and Clapham Junction. Without any splits that would be £10.40. With a split at East Croydon it's £6.00 to East Croydon + £2.70 = £8.70
- Taking the Elizabeth line via Farringdon, but splitting your PAYG journey at both Hayes & Harlington and East Croydon: £4.80 to Hayes & Harlington + £4.15 to East Croydon + £2.70 = £11.65
It all depends how much hassle you're willing to accept, to be honest.