How long do you have to cook wild morel mushrooms for them to be safe?
I've looked through a number of recipes, and the vast majority of them indicate that you should cook the morels thoroughly (preferably in butter) first, before using them as a pizza topping or in an omelet.

I did find at least one recipe for a morel omelet that did not call for pre-cooking the mushrooms, however.

I must admit that I did my research a bit late, as I had already decided to risk it and made an omelet with morels, as I had not yet received any answers to my question.

I added the morels to the raw egg, rather than putting them in as a last-minute filling just prior to folding the omelet, so they did cook a bit during the process.  The result was actually quite delicious (I also used some fresh garlic, chives, and Gruyere cheese), and I did not become ill.

However, it does seem that some people react differently, and alcohol consumption can greatly enhance any negative reactions to wild mushrooms.

Given the information I found on the Internet (none of it terribly authoritative, as the vast majority of quality information was on small sites maintained by wild mushroom hunting clubs and enthusiasts), I would not repeat my omelet without pre-cooking the mushrooms, nor will I make pizza without pre-cooking them.

The consensus seems to be that they should be sauteed once until "thoroughly cooked".  At least one site (amid heavy cautions) specifies that this is usually 8-10 minutes, although I suspect that this is for intact mushroom halves, rather than small pieces (morels should always be sliced lengthwise to ensure that you can remove all the insects from the hollow center).

It needs to be stressed that even with the proper cooking, it seems some people have strong reactions to wild mushrooms, so use caution and moderation when trying them for the first time, and do not try them with any form of alcohol until you are sure that you can eat them without problems.