And to think that some people complain about having too much zucchini (Cucurbita)! I suspect that your zucchini rot might be a disease that is common among squash and other plants in the cucurbit family: gummy stem rot. Seeds and soil carry the disease; but because you say that you have no problem with other squash and gourds, I'm guessing that it's your seeds that are infected. You may also have chosen a variety that is not resistant to the disease. Stressed plants are more likely to contract diseases.
To cover all your bases, grow zucchini plants where they've not been grown before, avoid high-nitrogen fertilizers, and mulch the plants so the fruits do not sit directly on the soil's surface. Mulch also prevents dramatic fluctuations in soil moisture, which cause plant stress and blossom-end rot, another common disease of cucurbits. Excess buildup of salts in the soil can also cause blossom-end rot. To help leach the salt from the soil, water more thoroughly each time you water, but let the bed dry out a bit before you water again. Here's hoping you have the experience of too many zucchini next season!