Well, do we want to advertise openly, or be just a little enigmatic that we're the ones behind it? And as for the venue, if we are going to use the Hakurei Shrine (which we really should, if for no other reason than to fluster Reimu) are we going to advertise this upfront (possibly arranging this with Reimu first) or leave the final location of the tournament a secret until shortly before it begins? This might interfere with logistical setup and catering somewhat, but perhaps we could just simply gap in the food and half the infrastructure right before we're ready to begin. Well, and there's always Reimu's reaction, but we can possibly wing that one, given that what we're doing doesn't seem harmful enough to promote more than an irritated response. I am not entirely sure whether it is better to give her time to object in advance (so that we can possibly straighten that out) or to leave it until it is hopefully too late for her to complain too loudly (unless she decides to be quite vehement indeed)
In terms of advertising, we can probably gap fliers to select people we hope to participate, or locations where they will get noticed. Aya might be of use in this regard without needing to even ask her, as I can see her considering a 'mysterious tournament with the relic of a powerful and old onymouji as the prize' as something newsworthy, perhaps especially if it was not immediately clear who was arranging it.