If my thread breaks using this heavier Cotton thread, what do you recommend?

According to Cindy Losekamp, Sew Artfully Yours, who has been using the 12 wt. Cotton thread for many years for both decorative stitching and for her computerized embroidery designs, you may need to tighten your top tension! I know that's startling, but she has a "big dog theory" about this thread which is basically, "when walking a big dog (12 wt. Cotton), you need to hold on tight or the big dog will run away with you", which means you need to "restrain" the thread more as it passes through the tension. This may not be the case on every machine out there, but it seem to be true when doing computerized embroidery with the Sulky 12 wt. Cotton.