How to get a thicker soup from watery tomatoes?

One thing you can do is dry off much of the water by slow-roasting the tomatoes in the oven first, similar to what I do in this risotto. I think you will get a more complex flavor than if you boil the heck out of them in a pot to reduce. I was also going to suggest pureeing them and then hanging them in a cheesecloth bag to drain the water, but you'll lose too much flavor that way.

You can add quite a lot of tomato paste/puree but this will mask the fresh flavour of your tomatoes.

I think I'd just reduce the soup down once it was made or add carrots. Carrot flavour really complements tomato soup and many tomato soups recipes require carrots. The starch will then help you thicken the soup.

One trick I use for thickening soups is instant mashed potatoes from a box (we also freeze leftover real mash for soups, but it doesn't work quite the same way). I would think you'd want to be careful about using too much in a tomato soup, but it might be worth considering if your soup only needs a little help.

Add potatos! You generally won't taste them but they'll add thickness to your soup.

It might be too late to help you, but for others -- consider not using the whole tomato.

Rather than using whole tomatoes, if you slice them in half (through the equator, not along the stem/blossom line), and then take out the gel in the seed cavities, you'll have almost all 'tomato flesh'. I just use a clean finger (shove it in the cavity to loosen the seeds, then a flick of the wrist over a garbage can to extract any bits still left).

If you're going to be peeling the tomatoes, too, peel first, then take the seeds & gel out, but it's going to get messy (and I'd work over a garbage bowl, not the garbage can directly, as they're going to be slippery). Of course, if you use Michael's recommendation, you don't have to separately peel the tomatoes, as the skin will come off easily after roasting)

I made a tomato broth as the recipe called for and loved the taste, but it was thin as broth should be and I just wanted something thicker with more body. So I added a 6 oz can of tomato paste, 1/2 cup of cream and another pinch of salt and white pepper to the 2 1/2 cups of tomato broth I had already made. It worked out perfectly! it was thick and creamy just as I had wanted with great tomato flavor.

Corn starch shouldn't effect the flavor much. Or try wheat flour which is usually handy, though that does have the more "bready" taste. This is basically the same as the roux comment. For variety and less flavor impact try rice flour or starch.

If you've already got it mostly done and you're on a tight schedule, adding one or both of those will thicken any soup/sauce after simmering for another 2 minutes. I must have rescued a hundred dishes this way.. sauce mostly, but also an occasional stew, chili, or soup.