Not sure why, but I can't modify/balance this equation I'm working on modeling a few reactions for my research. For example: 

$$\ce{CO2 + H2S + CH4 &lt;=&gt; CH3SH + H2O}$$

was one I grabbed from the literature. However, this reaction is taking place in the aqueous phase around neutral pH, so most of the $\ce{CO2}$ will actually be $\ce{HCO3-}$. So in an attempt to model modified versions, I swap out the $\ce{CO2}$:

$$\ce{HCO3- + H2S + CH4 &lt;=&gt; CH3SH}$$ 

I've tried a redox-equation balancing approach but this hasn't really gotten me anywhere- sulfur doesn't change oxidation states. 

I think my brain might just be fried, but can anyone lend any insight on this?
For starters, You have a problem because of a lack of charge balancing. You should also consider that at neutral pH $\ce{H2S}$ is present as $\ce{HS-}$ and $\ce{CH3SH}$ is present as $\ce{CH3S-}$.  Modifying the reaction to account for charge you get:
$$\ce{HCO3- + HS- + CH4 &lt;=&gt; CH3S-}$$ 

This will give you a start.  The other piece that will help is what the $\ce{HCO3-}$ molecule becomes. For the sake of being able to provide an answer I will assume formate ($\ce{HCO2-})$ is formed. Thus the reaction is now:
$$\ce{HCO3- + HS- + CH4 &lt;=&gt; CH3S- + HCO2-}$$ 

We know that the molecule of $\ce{CH4}$ becomes $\ce{CH3S-}$ and the molecule of $\ce{HCO3-}$ becomes $\ce{HCO2-}$ thus to balance the lost oxygen of $\ce{HCO3-}$ and the lost two hydrogens of $\ce{CH4}$ we add water to the products.
$$\ce{HCO3- + HS- + CH4 &lt;=&gt; CH3S- + HCO2- + H2O}$$

This equation serendipitously requires no coefficients to balance.