Yes, that's by far the cheapest option. The £16.10 Anytime Return is very good value.
There are standalone validators in two places at Farringdon. First of all, next to the couple of steps between the southbound Thameslink and northbound Sub Surface (Met/H&C/Circle lines) platforms. Secondly, roughly half-way between the northbound Thameslink platform and the Elizabeth line - at the intermediate floor where you have to make a 180° turn to/from the Elizabeth line escalators.
Is that perhaps why another standalone wasn't placed for EL journeys on the southbound platform? I've seen that reader before and used it once, but its definitely not well signed.