Help to address a stinky fungus problem

Help Please - This year I have a problem with stinkhorn mushrooms in a recently created perennial border in my rental home.  I created this slightly raised border 2 years ago around a couple of conifer stumps.  The first year was fine but this year while sat in the garden during the summer our noses were assaulted by the most horrific smell which kept wafting over us.   

This continued on an off during the summer and drove us away from that part of the garden.  It was only on return from a holiday I discovered a mass sprouting of gruesome looking mushrooms with the tops covered with a foul smelling green slime.  My nose told me that these were the culprits.  Since August I have been digging out clusters of white egg shaped mushrooms.

I would really appreciate some advice from more experienced gardeners than myself.   My question is three fold really;

1)Will these mushrooms continue year on year now that the spores and mycelium are in the ground? 

2)If I dig up the plants, carefully wash off all of the dirt and re-pot them into new compost will they be ok (ie not carry the spores with them to other parts of the garden) or should I just take cuttings and seeds and bin the originals?

3) and finally, Is there any chemical / natural treatment for this type of infestation which will save this border or at least stop these pesky mushrooms in their tracks.  I rent this house so can't really go to the expense of grinding out the stumps which I guess would be the optimum solution.

I realise nature is only doing what it should by cleaning up unwanted dead wood, it’s just a shame it had to be that particular fungus that decided to take hold. 

At the moment my plan is to dig out everything.  Black mat the ground and mulch with gravel, then create some raised planters (totally off of the ground.

All advice gratefully received.Thanks