It is impossible to eradicate honey fungus. It is just something that you will have to live with. Google 'honey fungus' and go to the 'garden action' website which has lots of info and a list of plants most and least susceptible to honey fungus.

I've got the same problem in one of my gardens currently - we are about to get the tree stump removal people in to have every bit of wood, live or dead, in that area removed, including the two remaining shrubs which are alive. Once that's done, I intend to replant with, initially, mostly perennials (including Phormiums) that don't have wood, together with probably a Choisya (one of the least susceptible) to see what happens. Honey fungus comes in various "strains" and some are much more virulent than others.
RHS list of least susceptible plants is as follows:
Taxus, bamboos, beech, box, mallow, oaks, abutilon, actinidia, carpenteria, celastrus, cercis, catalpa, ceratostigma, chaenomeles, choisya, clematis, cotinus, elaeagnus, fothergilla, hebe, kerria, passiflora, phlomis, photinia, pieris, pittosporum, rhus, romneya, sarcococca and tamarix, plus most (though not all) perennial plants.