Impedance mismatches eg at output devices feeding input devices should not cause any damage. Only possible sound changes. Impedance mismatches at high power amps feeding wrong speaker impedances certainly can cause trouble. But we are not dealing with that here.
The Little Labs Pepper looks like a very cool device. But at your US dollars it is between $600-$700 ($1200 here in Oz) so it is one very expensive device. It does do a lot granted but you may not need all those features either.
Radial make a basic re amp box for around $99 your dollars and $199 for a more complex model that offers a few extra features. (which look useful too)
Apart from dropping the level right down from your interface to guitar levels a re-amp box presents the same high impedance an actual guitar does to the amp. This can effect the sound between the source signal and the very front end stages of a guitar amp.
And
Beeps no I am not a guitarist but I have had experience re-amping a few times and it can be fun and very cool to do.
And
BobF you have got a lot of pedals there. I am hoping you can totally bypass the effects loop
(where you have so many pedals connected) if you need to preserve the dry sound a bit more. Isn't there one nice guitar effects processor that does it all that just connects to your amp effects loop? Then you can just plug your guitar straight to the amp. (which might actually sound best)
For example you have got your guitar connected to the Wah pedal so the guitar output impedance/Wah input impedance/input stage combination is setting the sound for the whole chain that comes later. Your guitar might not sound its best plugged direct to a Wah pedal first in line like that. Have you thought of that?