Its a matter of what tripod mount you are using. Some are bigger than others. While a bogen hex plate could potentially give you issues, an L bracket from something like Really Right Stuff (Sony A7 L plate) appears to be designed so that it has a smaller than camera base plate on it.

I'm going to point out that this is not a "few dollars" and if you are asking this question, you likely don't have an arca-swiss style quick release plate tripod head.

Thats just one quick release plate. There are many others in the area style that are small. For example:

is a small generic plate on a rather small camera.

There are some rather small QR plates out there from Arca-Swiss such as a 32mm x 32mm plate (b&h) and a 48mm x 32mm plate (b&h). Given the option I'd be looking at the larger of those two plates because it provides more of a base for the camera to rest on (though I have to admit that I don't have a Arca-Swiss head to look at (I've got Bogen RC-0s which I know won't work for you at all) nor a Sony camera to measure to check on the tolerances).

Get a good tripod and a good quick release system and you won't have this problem. There are more than enough QR plates out there for the Arca-Swiss system that you will find something that works precisely. And given the funds, I'd really check with the RRS option mentioned at top because it is designed exactly for that camera.

---

That said, an old search finds extending the 1/4" screw on tripod heads. A home improvement store should be able to get you a longer screw and you put a few bolts and washers on it in hopes of providing enough support.

That last bit is key... and something you are going to have to watch out for. You are trying to move a rather heavy camera up a bit - so that it isn't in contact with the tripod head. This means that the stresses on the screw itself will be greater. You risk breaking off the screw in the camera with any solution like this.