I did tons of Western blots with SDS-PAGE onto membrane but never agarose gel.  How thick is your agarose gel?  Maybe you could give semi-dry a go?

I have no experience with DNA:protein complexes, but I would go for traditional capillary transfer (to avoid having to take into account the net charge of the complexes, etc), as used to be done for Southern blots.

Hi, to answer strictly to your question I study something in the past, about protein (only proteins) electroblotting from agarose gel, to analysis high-molecular-weight proteins; I attached some articles where you can find some suggestion about buffers and transfer. I don't known if these works can help you, I suppose that you known your protein of interest and you have antibody against it.

In any case there are, on the web, protocols about detection of proteins through EMSA assay (or other approaches), that explain alternative method for protein complex detection

I am sorry but you will find some underlined paragraphs in the files.

Thanks for this papers that help me.