I don't think Sto Vo Kor is only entered if a Klingon dies in battle, I think he just had to have led an honourable life. In theory I can even see a Klingon who was never in a winning battle, but had still fought with honour and glory, getting in.
If you had to die in battle, why would ANY Klingon ever take a post on the High Council? Or a diplomatic post? Or scientific? If you serve the Empire with honour, in whatever role, that has to count.
Klingon society would be unable to function if everyone HAD
to be running around in a Bird of Prey, gloriously fighting their enemies. If dying in glorious battle was the only way in, they would never have signed the Khitomer Accords at all, as peace would condemn millions of Klingons to never be able to enter Sto Vo Kor.
Or, are we saying there's a different Klingon heaven for clerical staff?