I would give the methode with the 2-pole Sallen-Key Filter a try, providing a settling time of about 0.1sec. So, choosing Cav=300nF and C2=C3=680nF, or so, according to datasheet, could result in a total error of about 1...2%.

Check it out by comparing the result of AD637 with the direct computation of a stored signal from a fast data logger.

Of course, you must sample the output of AD637 often enough during the Gaussian pulse to get the true shape of your signal.

Kai Klaas