Ground elder

Having just taken over a large, once beautiful garden this summer we have spent many days killing, then digging out ground elder roots. Even after digging twice and then raking firmly we know that some roots have escaped, some are trapped under camellias and rhododendrons and some are still in the grass surrounding borders and beds. 

Is it wise to grass over the large spring garden bed so that escapees can be dealt with by the mower and where the shrubs are with weed killer every late spring? If not what? I do not wish to dig the bed over again as it took days to do this year And I am not a young gardener!

Unfortunately, the weed is throughout the garden. 

Any ideas would be most welcome.

  Thank you