Saving jpg when working in Photoshop 16bit mode

Whenever I do any post processing in Photoshop I work in 16 bit mode and save my work as a PSD. To display any of this work on the web though I eventually need to save it as a jpg. Lo and behold, that option does not exist in the Save As dialog if you work in 16 bit. This particular "feature" bugs me to no end. I know jpg is 8 bit, but it can't be that hard to do the conversion automatically and save. Thus saving jpg always requires an extra step which is to convert to 8bit.

My way around this repetitive tasks was to create a jpg saving action. The extra benefit is that I get to skip the rest of the Save As dialog box too, and I get to save a jpg with one click.

I recorded an action where I did an 8bit conversion and then saved a file. For the file save the action saves the file type, quality, and destination directory, but not the file name itself. Thus when I run the action it uses the current document name for the file name. Since I've already saved my work as a PSD it already has the naming convention I use, so the only thing I have to do is remove the word "copy" from the end of the name (another photoshop annoyance).