Were I in your shoes, I'd just book the cheapest company every time.

With Emerald Club, you do not get an upgrade benefit. The best you can do is book a midsize and hope to find a minivan on the Emerald Aisle, but that's a risky bet.

You can focus all of your business with National and probably hit Emerald Club Executive status, which requires 12 rentals per year or 40 rental days. This gets you a guaranteed one-car-class upgrade (actually, you book what you want, and the system automatically charges you for one car class less); however, I am unsure if this extends to specialty vehicles like minivans (a test booking I just did at MCO seems to indicate not). Also beware that unless you can hit Executive Elite status (25 rentals or 85 rental days per year), any free days you earn with National can't be used for minivan rentals.

Given that, I don't think it's worth pursuing status with National. Other rental companies won't really work for your level of business, either, as the other premium brands (Avis and Hertz) require you to hit third-tier status to qualify for the free upgrade benefit (and it likely won't get you into a minivan; you'd be looking instead at free upgrades to premiums or possibly SUVs unless perhaps you call ahead and specifically ask about an upgrade to a minivan).

So, I'd just continue booking the cheapest van possible. It may be worth signing up for the rental agencies' rewards programs, though, so that in the event you do earn enough credits to qualify for a free day, you can use it, but I wouldn't go out of my way to earn credits or status.

Do note that Dollar Express Rental Rewards free day certificates and Thrifty Blue Chip free day certificates can both be used for minivan rentals. It takes 16 rental days to earn a certificate, though, so the return on investment is small (unless you get very lucky and play your cards right, earning on super-cheap rentals and redeeming on expensive rentals). Note, too, you'll be responsible for taxes on those free days.