I had a similar area of lawn which had been destroyed by badgers. I contacted gardening professionals and like you, all reluctant to reseed but happy to returf. I was told that resending can be problematic and not always effective
So I did it myself - got rid of all remaining turf, scattered the seed and then dressed with a fine topsoil (‘which also helps to prevent hungry birds eating the lot). The most crucial bit was watering every day. I was also told, when watering, to try and simulate rainfall by pointing hose in air and letting water droplets fall from some height - could have been a load of bollocks as the advice came from a ‘zen’ gardener!
i now have a full functioning lawn which so far has resisted any further badger attacks
good luck with whatever you decide to do