So after a high speed 30 mile road ride, I'm getting pain in my right achilles tendon whenever I pedal (it starts after about 2-3 minutes of riding)

Is it still safe to ride my (4.5 mile each way) commute without damaging it further? Should I take precautions like abandoning clipless, lowering my seat, etc? I've already slowed my pace from ~18mph to ~13mph.

I wouldn't abandon the clipless pedals, but how did you decide where to put your cleat?

It's roughly under the ball of my foot, because that's the center of the adjustment range on the shoe (Specialized MTB Sport).

Sounds like you just have some microtears, but I would see your doctor and make sure you don't have a ruptured tendon.
He will likely tell you to stay off the bike for a while to quicken the healing process. This type of injury usually takes a bit of time to heal. Get some good stretching exercises. Bike adjustments (seat / clipless, etc.) will not really help you with this. Ibuprophen will.

I would try moving the cleat back a little on the shoe. I had sore Achilles issues for awhile back before clipless pedals when I was using a set of toe clips that were a little shorter. The problem went away when I switched back to longer clips

You can pull a tendon for various reasons even if everything is set up properly. It could be just one off incident. Just give it some time to heal: ice and compression helps and some Ibuprofen to stop any inflammation. Unless it's swollen and hurts so badly you can't walk easily I wouldn't see a doctor yet.

A very gentle stretching before riding might help, nothing too strenuous though, although I don't bother. Riding gently at first is enough stretching for me. And keep those tendons warm during riding to prevent injury.

I would double-check cleat location and seat height. Also find a knowledgeable physical therapist. Achilles can go south and take for freaking ever to heal. Really, like months and months. And I stress the 'find a knowledgeable p/t' part. (or chiro or whatever). All the achilles stretches in the world it turns out were the wrong thing for my instance, they would have just kept making it worse. p/t gave me different exercises farther removed from the source that kept me biking throughout and solved the problem.

S'truth. My lady did hers over the course of last summer playing soccer. It only ached a bit, so she kept taping it up and wouldn't stop playing; by the end of the summer she couldn't even go for short, easy runs. Even with a winter's worth of rest and physical therapy it's still bothering her.