I'll try to write my comments as an answer.
First, I would say that your assumption is correct,
hubiera goes into
tuviera. And that's it.
On a personal remark, I don't know if this method is helping you but I don't think direct translation is a good idea when learning languages. In particular, subjunctive tenses are kind of dificult to translate directly so you're going to have a rough time with it. I would look for subjunctive tenses in spanish, they are constructed according to rules, it's not random.
What I mean is that you have to use
tuviera instead of
hubiera because you're trying to say "another thing" so you do not need
haber as auxiliar verb.
You can "tener" A LOT of things (hunger, anger, dissapointment, etc). It does not have to be a real object but yes, if you have/would have a real object then you tienes/tendría o tuviera. Since
hubiera is working as the auxiliar verb (just as have is used for present perfect as auxiliar verb) it is needed for some verbs that use "hubiera". Since
tener is not one of the verbs that need auxiliar, you can use
tuviera (and this is what I mean when I said "you are trying to say another thing")
Hubiera works for subjunctive as auxiliar conjugation of
haber, but you also have
haya and so on check es.wikipedia.org/wiki/Modo_subjuntivo
Also, keep in mind that subjunctive mode is one of the last things that native people learn during elementary school and it is seldom used correctly because of its difficulty.