Suggestions for an experiment?
This is a bit hard - most possible answers you still aren't going to like, but I'll give you three suggestions. 

It sounds like you want to take something with a mathematical model and try to modulate it with molecular biology.  

It seems unlikely that I can really give you a specific project, but there are four sources  I will recommend you look at.  

I think I'd suggest the further limiting assumptions:


you want to work with E coli - its the easiest and most readily available organism to work with.
you want to work with a system that is self contained within a single plasmid - so it relies only upon 2 genes to act, 3 at the outside or you will have issues getting it all to work.   
you want a mathematical system that already has a well fit model that  you will peturb.  building a new model might be a bit of a big first off project.  (but who am I to tell you what to do - these are just suggestions).  


The First suggestion I have is Jeff Hasty at UCSD.  He has focused a lot on oscillating gene circuits.  He has simple systems that might be reproducible with a small lab, most recent work that combines a GFP oscillator with LUX is pretty cool. Both oscillators and LUX are independently good systems to work with. .  I've been a science fair judge and I can tell you, just reproducing one of his systems would be an impressive lot of work

Another body of work to look at is Adam Arkin. He has looked at lots of circuitry component candidates.  Articles such as "The hunt for the biological transistor" might get you thinking.  This is a broader body of work, and so it might take a while to get an idea from it. 

Third, if this is boring to you and you want to look more broadly, you can look through the iGEM competitions.  These are projects with oscillators and bio synthesis systems which sometimes have mathematical models associated with them.  The big advantage here is that you might be able to start or join an iGEM team and then some or all the plasmids will be made already - mol bio gets very expensive if someone doesn't gift you some materials.