Update: I think it's the Cuemix software application that comes with the Traveler interface that's getting in the way of this. It's always been annoying because it adds more complexity, I'll contact MOTU techies.

I am thinking it is either the MOTU's basic hardware output level controls or, as you say, the dsp.
 
If it were Cuemix it ought to be really easy to open Cuemix and see what's up... make sure you scroll all the way to each side to see everything.
 
If it is the hardware control, you have (at least on the older models) to push/scroll through a selection process and then you can spin the knob on the output for a particular selected output. That may be combined with the dsp on the newer models.
 
It's going to be one of those "oh yeah" things.
 
best regards,
mike

>push/scroll through a selection process and then you can spin the knob
I remember that, you'd think there would be a default nominal level - will check.
 
In Cuemix, there's nothing to see because nothing is happening. Nothing is muted, disabled or turned to zero. Once I get this down I'll save Presets and Profiles wherever possible.

Just to jump in here, I'm not sure what "Sonar's External loop Feature" is, I guess I could look it up, but..
 All I do is assign the track output directly to Interface Output 3/4. 
Patch it to what ever,  and bring it back to re-record. 
I've never found the signal to be anything other than a standard line level. 
I could turn it down in Sonar using sub output faders for 3/4 but haven't had to yet. 
 
I have 3/4 hardwired right now to my Yamaha 01v Mixer to use for additional monitoring as well as I occasionally use the 01V effects. I have also run it into my Guitar amp, miked it and re recorded the track. I found no latency offset at all. And I have a Tascam interface which has so so drivers. A Motu should be way better? 
 
As far as using external efxs goes your going to be blending them with the original so it's no different than 20 years ago using an analog desk system, right? 

Cactus: Your method was my first thought and the next thing I'll try but the External Insert looked promising. It allows you to insert any hardware device as an effect and theoretically re-amp a clean track with measured latency compensation. I'm not getting anywhere with it because I'm not sure it really works very well and I have vendor software in the way.
 
I've got a question in with MOTU techies but if they're baffled, I'll dump the External Insert option.

Summary:
A straight round trip works just fine. Send the clean guitar into the processor and record the result to a new track in Sonar. You have to pull the resulting clip back but that's not really a big deal. The only thing I think I'm noticing, is that playing the guitar into it normally doesn't seem to sound the same as sending it the prerecorded clean guitar. It could be my imagination, I'm doing some tests.
 
The External Insert may be useful to some because you can save a preset and theoretically, Sonar can measure the latency and automatically compensate for it. In reality, as Mike mentioned above, you would need to perform the latency measurement every time you changed a patch because a different chain of effects would take a different length of time.  
 
The Line 6 PODxt Pro has INs and OUTs specifically for reamping so you don't have to worry about pulling physical plugs out and re-patching them, that's really handy. You only have to change the driver mode. My Roland GP-100 doesn't have that capability so I have to do it manually.
 
You can adjust the sound in real time if you're using a virtual guitar like Electricity or Shreddage. You can send the output of the virtual instrument straight into the round trip, you don't need to bounce it down first. Now you can change velocity settings in the MIDI data on the fly and hear the result immediately.
 
 
1) Set the output of the virtual instrument to the input of the Guitar Processor (i.e. OUT 1 to Front Panel IN)
2) Set the output of the Guitar Processor to another input on your interface (i.e. OUT Left Mono > IN 1)
3) Set IN 1 as the source for a new track (i.e. Track 2) 
4) Select the section and set it to Loop. Press Play.
 
Now you can hear the result of the round trip playing on Track 2. Select the MIDI clip and enter new velocity values as required in the Event Inspector toolbar. You can immediately hear the response to more or less muting (for example). 
 
rev