Is Mixture the best way to model a superposition of distributions?

I’m still learning the ropes with pymc3, so I may be approaching this in a completely useless way! I’ve got some data that appears to be a superposition of two exponential distributions and a more or less uniform background. My data is limited to a finite range, and I don’t want to bias the estimates due to this fact. I’ve decided to try to use a Mixture. Is this a reasonable approach? Mixture seems to require cores=1 , which makes this super slow. Is there a better approach?

You can see my attempt to generate simulated data that more or less matches what I’m measuring, and the pymc3 analysis, here:

Thanks for any advice!