I would definitely reinstate the litter tray (the weather isn't that nice, I expect Tigger prefers the comfort of indoors :/) and carry on using the biological washing powder, perhaps double strength, on the soiled sheets. I think most people on here say "ignore messes inside" but personally although opposed to the old "rubbing noses in it" I would usually show the animal the mess they've made, register disapproval (no) then taking the naughty party, I pick the mess up and put it temporarily where I would prefer it to be (ie litter tray, flower bed) to show them.
Never tried it myself but some say try two litter trays (if you are already using one and it's not working)
Hope you can sort it out, it's not very nice! My friends dog used to prefer my bed back when I lived in a communal house. I used to shut the door... so of course she just sought out other people's beds! In the end, it was the taking it outside that sorted it for her... the smell of their own poo is like a little sign to them saying "toilet here!" That's why we use the bio powder to clean as well... it actually kills the enzyme in the poo so that the smell is totally eradicated.