I don't use 1 shot colour cameras, but maybe the answer is to use the non-Ha sensitive camera to give your basic colour and then create a synthetic luminance from the colour to which you add a SMALL amount of the Ha data (which will primarily be only in the R channel of the Ha sensitive camera). You also want to add a SMALL amount of Ha to the other red channel and then regenerate the RGB. There are tutorials all over the place describing this type of processing. My favorite way of doing this is described by Adam Block using Photoshop. For sure, too much Ha will overwhelm all the other data as you have already observed. In my opinion, Ha data is data that gives very interesting detail...but too much and the reds will blow out everything. Really, I think you just want the detail.
Peter
EDIT: " Modified cameras with enhanced hydrogen alpha sensitivity result in hydrogen alpha dominating the images of nebulae, hiding the multiple colors and processes present. An unmodified camera shows these colors and their varying intensities better so you can discern chemical and physical processes and composition."
Interesting read:
http://www.clarkvision.com/articles/...rstellar.dust/