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. :)]
I'm not an expert, but, from what I know, your experience is quite valuable.  Even if you had computer science research experience, there's a good chance that what you would actually end up doing in a PhD program is far from the domain of your undergraduate research.  

If you're still worried, note that theoretical computer science is all mathematics.  I was an applied mathematics and statistics major and am currently taking a graduate course in approximation algorithms--it's literally a graduate course in theoretical side of applied mathematics.  Other theory courses in automata, computation, machine learning, etc are also all math courses, but in the computer science domain.  I actually think that your math/research background, if anything, is a huge plus.

What PhD programs are really interested in is whether or not you have done research in any discipline (preferably math/engineering for CS) and if you enjoyed it and showed an aptitude for it.  You're ahead of the game, don't worry.  On that note, if you know that you want to do TCS research, you could start now.