I think the reason people don't want to use the molasses is because of the sugar content. I assume there's probably more sugar in the molasses beet pulp than non-molasses, so this could probably help. But that's just a guess, so double check that info!
I use Standlee Beet Pulp Pellets, here's their product description from off their site:
Standlee Hay Company provides quality products from outside producers such as Beet Pulp Pellets. Standlee Hay Company Beet Pulp Pellets originate from Idaho grown sugar beets. These pellets are made from the fibrous material (beet pulp) left over after the sugar is extracted from the sugar beet. Pellets are formed from dried sugar beet pulp with a small amount of molasses added during the drying process. These pellets are an excellent source of digestible fiber, with relatively low crude protein content. Beet pulp pellets are great for horses known as hard keepers or other animals that need to gain weight. Additionally, beet pulp pellets are a great choice for a convalescing horse or while recovering from an illness or surgery. Standlee Hay does not add molasses to its beet pulp products; the molasses is a result of the drying process at the sugar factory.
Their Beet Pulp Shreds:
Standlee Hay Company provides quality products from outside producers such as Beet Pulp Shreds. Beet Pulp Shreds, another product from the sugar industry, is very similar in principle as Beet Pulp Pellets. This product is an excellent supplement to a feeding regimen, adding a high digestible fiber. This product is higher in sugar, ranging from 10% to a high of 20%, when additional levels of molasses are added. Standlee Hay does not add molasses to its beet pulp products; the molasses is a result of the drying process at the sugar factory.
Since the Beet Pulp is from sugar beets, I don't think you're ever going to get all the sugar out. I certainly wouldn't feed them to an Insulin Resistant or Laminitic horse.