I'd think that using 1-3-1 zone is suicidal, especially for our team. 1-3-1 zone is a super perimeter defense and unless you have a super monster big-man, the opponents will just get too many offensive rebounds and go for easy lay-ups. Since we don't have strong big-men, I don't think there'll be a case where we'll use 1-3-1 zone.
Even with man to man, out perimeter defense is likely to be far better than our inside, and I guess the only case where we might use 3-2 zone is if the opponents had a very strong outside shooting and very low rebounding.
If you miss something in ID and have strong OD, I agree that best defense is man, to put pressure at perimeter and limits damages (I did it for so long time with my team...).
1-3-1 is a desperate defense, to be used where there is no option and with what you called "super monster big man" (Shaq 15 years ago). 3-2 without two good internal defenders can be critical, although can be used under certain circumstances: for instance, if the two tall men have very high RB, they are statistically closer to the board and will catch more RB's even with a worse team bonus. However, your opponent should play outside offense (or you would be fouled out), and have no such a good circulation (or ball will come inside as knife into butter).