I tried almost every preset.  On guitar, NONE of them have the same volume as a bypassed signal without cranking up the output gain, or maybe you can get close by boosting the EQ across the board.  But even at maximum drive, for various values of the sustain knob, engaged << bypassed if the output gain is +0 dB.  The only one that's in the ballpark from the get-go was Crawdaddy, which I think was already at +4dB, but even that seemed like it really needed to be at closer to +10 dB.

I explored the input gain, it was set to 0 dB.  Increasing it didn't seem to help, which makes sense according to my understanding of the process—if I increase the input gain, that's just slamming the circuit, if it's already quiet due to weird compression effects that wouldn't help much.  Again, maybe that assumption is completely wrong.

I could try to record some video/audio if that would help.

 

Sure audio/video could help. 

It's still digital gain, so we have to clip in a nice distorted way so as to never reach 0db Full Scale value.

A little more explanation: Since the base gain swing on the distortion curve about is so huge (up to 32 dB I think), we do some auto volume normalizing so we didn't have to have a huge swing on the output gain to make up for small and large of amounts of distortion.  Most distortion pedals have the gain and volume knobs, and this is really no different, we just created our own auto volume knob functionality and assumed people would use output gain to fine tune.  

It could be that your guitars have a very hight output.  In which case you're loosing some dB due to the asymmtrical gain curve, etc.  Another quick test to see if this is true: try your bypassed / active test with your volume knob down to varying degrees and see if it ever comes out the same that way. 

Alternatively, if the signal is low, you could be getting caught up a bit on the wrong side of the auto output volume stuff.  But increasing input gain on the H9 should help with this.  

Also, what type of bypass are you using (Relay, DSP)?  

You could also try increasing the Grit to get more of the lows and low mids into the distortion, this will raise the volume too.  If your guitar gets most of its signal in the lower range, or you play with the tone rolled off a lot,  I can see why Grit at 0 would significantly lower the volume. 

In general, this whole issue isn't anything I'd really condsider abnormal, just use the output gain like you are doing to normalize it to taste.  That's what it's there for.  I anticipated that people would have to use it much more on this effect than the others, it's just the nature of the beast.  If there's some other reason it bothers you to do this (does it make the algorithm unusable, etc.), I'll keep trying to dig deeper to see if there is actually a problem.