Airless sprayers have nozzles with apertures of different sizes. Have a few different sizes and experiment to find one that sprays at a comfortable rate with a decent pattern. Try different pressures, if the sprayer has an adjustment for that. When you're happy with what you're seeing on some test surface, then switch to the real thing.
Since you're new at spraying, perhaps forget about saving time by doing both sides. Just take your time to let the paint tack and flip the doors over. It's already a huge time saver just to be spraying.
There are ways to do it, if you insist. If you have a garage with exposed ceiling beams, you can screw in some hooks into the ceiling, and into the doors, and use string or chains to suspend the doors. I don't necessarily mean that the doors are hanging above ground, but just prevented from falling over, giving you access to both sides.
Doors often have recessed features, so you have to spray from various angles, otherwise areas in the "shadow" of the spray won't get coverage. Spray those inner carved areas first, then focus on the flat, outer surfaces.
Light is your friend! Spray in a very well lit area so you can spot problems right away, like the start of a run, or inadequate coverage. Bring in extra lamps.
Sherwin-Williams carries a door and trim enamel is quite good, by the way: the
ProClassic Interior Acrylic Latex Enamel. Is that what you're using? Even if you brush it on, it flows so well that you cannot tell. The downside is that the enamel is a little bit stinky with VOC's. Yet that is probably what allows it to dry fairly quickly, yet flow nicely at the same time.