I don't know why more isn't made of the lack of drivers on Thameslink. Perhaps Govia Thameslink Railway need to have posters and publicity criticising those who are causing services to be cancelled and causing misery for passengers!

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Taken to the extreme, that would mean GTR management ordering posters to blame themselves! As to passengers, they basically have no choice so GTR gets the money anyway.
I do not understand why the DfT is still not reacting in a customer-focussed way.
Why would they? With GTR operating in staunch Tory-land, they have nothing to lose, as it would probably take far more than the current indefinite shambles to sway the drone voters of the south east!
There is absolutely no end in sight for the shambles, as, even when the dispute ends (not 'settled', but ends) there will be deep-seated and very long-lasting rancour among the remaining staff, leading to an almost permanent animosity between the crews and whatever TOC runs the franchise.
Short of a huge and embarrassing U-turn, along with some major sweeteners from HMG for the staff (which obviously won't happen), I can see no course of action that can/will restore any semblance of reasonable service (not just the actual physical running of the scheduled trains, but all the associated passenger care elements - ticket checking, information provision, etc.) for many years.
Sorry to be gloomy, but I can simply see no way out of the mess short of a change of HMG, which also, sadly, is not going to happen.
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And they're not even working to rule yet (officially)
As far as I know, Thameslink drivers won't be 'working to rule' - it is only Southern drivers that will do so.