Not really. I have noticed that if I don't ride for more than 3 days, my legs do hurt more than if I had ridden at least some, but I've never had cramps. My wife has night leg cramps that seem completely unrelated to cycling, quite random. However, the more frequently she rides, the fewer night cramps she has.

My guess is that the doctor won't have a clue. Doesn't sound like it has anything to do with the sciatic nerve. Obviously something to do with the riding, though. You might try not letting more than 2 days go by without riding. Vague possibility that riding is exhausting some micronutrient, but you haven't figured out what yet. Seems unlikely.

By any chance have you reduced the salt in your diet?

Try carrying 500mg Tums with you, chew one immediately upon onset, another if it doesn't go away immediately. That's just a palliative, but it helps prevent the muscle injury which cramps cause.

Calcium? You drink milk, eat dairy products? I take a 1000mg calcium/500mg capsule twice a day, plus I do eat a fair bit of dairy.

Can't think of anything else.