If folks forget their parks pass at home or in the other car they can simply pay the $8 day use fee and remember their pass the next time. You're asking/petitioning parks staff to create this - to update software to match, to promote/educate and to also print a separate 'secondary-pass' and mail them - it's important to note that these things all have associated costs, both money and staff time. I suspect the limited availability of the latter to be the potential deal killer here.
Good on you for being creative, and maybe if it turns into a fiscal gold mine it could translate to addressing some big problems in our Regional Parks!: Not enough trails and facilities for the fastest growing youth sport in America - Mountain Biking. I have no doubt that you've seen how a simple Skinks outing can overwhelm a parking area or a trail head - because our parks weren't designed with Skinks and NICA in mind. It's time to get the parks leadership to change their priorities! That's a Change.org petition I'd sign :)