First, you can always take DME one-way (to/from airport to your hotel), so long as it's the same day as your arrival/departure day from WDW. For example, when we did a split stay, we took a private towncar from MCO to our Universal hotel ($75 for our family of 4, including gratuity). A few days later, we took an Uber/Lyft XL from our Universal hotel to our Disney hotel (around $25 with gratuity, I think). At the end of the week, we took DME from our Disney hotel to the airport. You can just as easily do it the other way, though (DME transportation to Disney at the beginning of your vacation). To set up your DME transportation, you can call Disney to add it to your reservation, or use this form:
https://secure.reservations.disney.go.com/ibcwdw/en_US/dme/dmeform
As far as when to pick up Mears "orders," I don't know but I'm sure Mears would tell you.
If you haven't already booked your Mears transportation or can still get out of it, my recommendation would be to use a rideshare or private towncar/limo service instead when you travel from the airport to Universal and/or between Universal and WDW. At least price it out on the towncar/limo websites and rideshare fare estimators: it may be significantly less expensive, and in the case of a rideshare, can be arranged in minutes, without you having to be beholden to a scheduled pick-up time. As for private towncars, we've had good service with Orlando Airport Towncar Service (
https://www.orlandoairporttowncar.com/) and Orlando Limo Tours (
http://orlandolimotours.com/), both of which run $60+ gratuity for a one-way transfer between MCO and Universal. Happy Limo (
http://happylimo.com/), a sponsor of this forum, also gets consistently good reviews.
