I'm sorry edwardian, but tears of laughter are streaming down my face. But this is only because we have hundreds of odds and ends stored in our garage "which might come in useful one day" (and in 25 years they rarely have.) so I know where you're coming from.
I wonder whether a square of thick foam place on top of your washing machine would help anchor the tumble drier. If two bolts could be drilled into your wall, either side of the tumble drier with a an "O" in them, a nylon strap (such as used for securing suitcases) could be strapped round the tumble drier, and slipped through each "O" hole to anchor it.
On second thoughts, this is probable a similar botch up to what your husband is about to come up with, so perhaps better forget it! Hope you sort something out.