Making tomato mix thicker without surge in calories I got on trying to eating more healthy and as a part of that, I take a few tomatoes, cucumber and garlic and blend that into a sort of a drink.  It's far more convenient and quick to smash a bunch of veggies into a blender and mix the crap out of them, rather than slicing and hacking. It also scales better - making a mixaroo of 3 or of 5 tomatoes takes the same amount of time, whereas slicing time is proportional. So I'm aiming at eliminating any obstacles along the way to wiser food choices.
I'd like to make it less liquidish, aiming for a thicker texture. I've tried adding broccoli, cauliflower, nuts and seeds. I tried adding oat flower and soy protein powder. It gave an improvement but to be acceptably substantial, I need  to push in quite a lot, which kind of defeats its purpose.
Is there something very calorie thin but structurally dense that I could smash into my drink? Extra bonus if it's rich on fiber.
Your primary option if you want to add a thickener, you can use any hydrocolloid you wish. I will not list them here again, since it isn't necessary that every single question on thickeners on the site gets the full list. You can download Martin Lersch's free reference book, Texture: a hydrocolloid recipe book, and start experimenting. I can also not tell you which one will be the best for your case - they all produce different textures, and it depends on your personal preference which one to use, and anyway, you have to see which one is accessible for you.
A second option for getting any tomato based liquid thicker is to either cook it down on your own, or to replace some of the fresh tomatoes by concentrated tomato paste.
The third option, deseeding, was already given in Keith Ford's answer.
And you already mentioned the fourth, bulking up with dry ingredients such as your soy powder.
I would say the four together give you a pretty wide range of alternatives, try them out and see which one you can best live with.