I have a few varicose veins, a menopause gift. Mine are pretty mild, not all lumpy like pictures I've seen. I take 2T ELOO and 1/2T fishoil, and they haven't gotten any worse, although some surface veins got more visible since my recent surgery. I wish I could answer your questions, I thought ELOO made veins better, but whether it could be the oil is a doctor's realm. I wore compression stockings after surgery, and that is a possible solution. But especially since they hurt, I think you want a medical opinion.
On the other ways to get flavorless calories, I've been trying exactly what Marianna is suggesting. I noseclip oatmeal with cottage cheese for breakfast, and a protein shake for lunch. I'm not good at noseclipping food that needs to be chewed well, but I've done other soft foods noseclipped, too. It makes me eat slowly. I've only been trying this two days, to get back my AS, and I think it is helping. Noseclipping was never as good as oil foe me, but it does contribute.
We have a couple people here without gallbladders who couldn't tolerate oil well. They took it in smaller doses (no more than 1T at a time) and closer to meals -- like an hour after a meal, or in a crazy spiced or noseclipped smoothie. You've done so marvelously well, I hope you find a good solution!