Is there any other way to prevent this, perhaps by using a step-up ring? The 40mm is one of my most used lenses and vignetting isn't an option for me.
The Lee adapter rings can come in normal or "wide angle" versions; the latter sit further back on the lens barrel than the normal versions, and are designed to help avoid vignetting. However the 86mm version unfortunately doesn't come in a wide angle version, hence the vignetting issue. It is unclear from that blog post whether the vignetting is only present with two filter slots used on the filter holder, as he does in the pictures (note: the Lee holder is modular in its assembly, and you can vary the number of slots from 1-3). With a single slot it may not vignette, but that may be limiting if you want to use more than one filter at a time (I use 2 slots on mine fairly often).
Barring that, you could hand-hold a filter in front of the lens (not ideal, and could well scratch resin grads), or look into some of the larger filter systems, such as the Lee 150mm system, or the Cokin X-Pro 130mm series. They start to get pricey though.