For years I used a stand alone computer diving a Classic KISS. No issues. then I plumbed a Shearwater in, no issues.
With my JJ, I just have a stand alone backup computer/. It is set to 1.3 ALL the time, no need to change it about and it will normally add a couple of inutes to deco.
I dive my JJ as a hybrid, so have no issues with running it from the HUD. If both go down, it's hihgly likely you would havae lost the signal to a backup computer that is blumbed in as well, so it all becomes a bit academic.
Best thing is to say,
'***k it', and go diving...
cheers
Andy