graduate admissions - Does research experience in a different but related field help in PhD application? (Pure Math->TCS)

I think the title itself is a good summary of my question.

But to make the situation more specific: I am a double major in math and computer science, and would like to apply to PhD program with theoretical CS as primary research interest. I am well aware that research experience helps a lot to show the committee that one has research potential.

All other academical records of mine are in decent shape so I want to shoot for the top programs. Now I am writing my SoP and here comes the problem: I have only non-TCS research experiences.

What I have in hand are:

1) serious pure math REU (not just expository) with a recently submitted paper

2) technical work (implementing and benchmarking) new numerical algorithm (scientific computing) with tech report

I was planning on doing a senior thesis, but my potential advisor is on a leave so it didn't work out. I went through the old questions and only found one related question. But I guess in my situation, it is worse because I have only research experience in entirely different subject. Although I am very proud of what I did, it is hard to sell them in SoP.

I always thought I don't need to do research in the exactly same area to what I want to do in grad school. Plus trying out interesting areas are fun. But it seems to me now that it was a very bad idea.

Doesn't "I wish to study a_0,a_1 and a_2 in A. I have done research in B and have been a trustworthy cheap labor in C. B and C are somewhat related to A, so I think I will do a decent job in A as well." just sound miserable?

[Thanks for reading - I know it is a bit long. Also I do apologize in advance if this question violates the rules - it is my first question ever. :)]