I have Nyvia II ready to hit the flower room again and was going to ask ya
Oh I did not include the factor that you of course still have Nyvia II and can bc in my previous reply...
Yeah man, sounds like a good plan.
Imagine a recessive trait in Nyvia II, let's call it aa.Crossed with GSC, which for example has BB, you get all Ba plants (typical F1 hybrid of two x homozygous), and none will express the trait.
If you cross one of those F1 Ba plants back to the Nyvia's aa, you get 50% Ba, and 50% aa. I.e. after the backcross roughly half the offspring would express the recessive trait again. If you pick one of those aa plants from bx1, and cross that to Nyvia's aa again, all the bx2 offspring would have aa and express the trait, and it will be the same in every generation thereafter (not in 100% in reality fortunately, because of chromosomal crossover new combinations will arise).
If GSC has for example Bb, however, i.e. is not homozygous, the percentages will be different in the first cross, not 100% will be Ba, and then you can't see the plants in the Bx1 that have that recessive 'a' gene. That's why I suggested using the plants from all 5 seeds regardless but if you are going to backcross it doesn't even matter that much.
In reality there are a lot more genes and some will be homozygous and some heterozygous so the above is basically per trait.
I know it's long, but I highly recommend reading my posts in the cubing myth sticky in this thread. The keypart is to use multiple males, i.e. cross a population back to a plant, not one plant to one plant. However, a small number of males in backcrossing can be easily offset, by doing an additional backcross gen. A step extra perhaps but from a better starting point for your purposes. I.e. even with one male Nyvia x (Nyvia x GSC) is better than Nyvia x GSC as a starting point for backcrossing. So it may take an extra bc to get where you want to be, but as long as you 'can' backcross to Nyvia II you don't have to worry.
The real challenge is to get those same genes in the same homozygous or heterozygous combinations. For recessive traits that's actually easier because a recessive pheno has only one genotype (homozygous, aa) while complete dominant has 2 (AA and Aa both express as the same pheno while you want AA for true breeding). In other words you can 'see' the genotype of recessive traits making it easy to select.
Autoflowering trait being a good example, auto x auto is aa x aa is all aa plants. But if you need to breed photos from autos... i.e. cross PP with aa, you get all Pa in F1, which are all photos, and in F2 you get PP, Pa, and aa, from which you'd have to pick two PP to create only photos while PP and Pa express as the same pheno (both photos) so you can't see the genotype. If you pick one PP and one Pa (both photos) you get all photos too but 50% will still be Pa and carry the auto gene. If you then pick two of those Pa genotype, photo phenos, for the next gen you get that same F2 ratio again of both auto and photo and all three genotypes.
The way to test whether it's PP or Pa is a test cross, either to a known homozygous, or selfing. You could gain a lot of insight from doing the latter. Self Nyvia II, grow out a bunch and for every trait in the offspring that is the same in the Nyvia II it's likely homozygous (i.e. you selfed AA with AA so you get only AA, same for BB-ZZ and bb-zz :). For every trait that shows 2-3 different phenos in the offspring you know it's heterozygous in the Nyvia II (i.e. if Aa in Nyvia than selfed you get the typical F2 ratio, 25%AA, 50% Aa, 25% aa. If complete dominant AA and Aa are the same pheno, but aa will be different. Essentially, selfing it is obviously an easy way to see how stable it is.
You can learn that same info over time crossing in or back, selfing is just faster and the ideal starting point for any breeding project.
When you backcross to homozygous, the offspring becomes more homozygous. If you backcross to a heterozygous, you create variety. Knowing what traits are homozygous in Nyvia can prevent getting into an endless loop of F2 ratios for some traits.
At some point, to get the best results, closest to Nyvia II, you may have to cross two (different) siblings from the same generation.
E.g. if Nyvia is heterozygous for some trait, let's say Gg. And you cross gg from GSC to it, you get 50% Gg and 50%gg, two different phenos. If you pick gg and cross it back to Gg again you get the same thing. If you pick Gg and cross it back to Gg you get 25%GG, 50%GG, 25% gg. If you pick GG from that one and cross back to Gg you get 50%GG and 50% Gg (which at least will look the same but unless it's the last generation you risk selecting Gg again for the next, and then get gg again). Instead, you can cross a GG with a gg to get the Gg like it has in the Nyvia II. This may simply not be worth it for some traits, and for most genes you won't notice, and for many it simply won't matter (it's all cannabis after all, many genes are the same and doesn't matter if they come Nyvia or GSC), but for some key traits however, it may be the necessary finishing touch. So again, saving the genes through backcrossing is easy, getting them in the same combination is harder. But as long as you create backcross generations you will be able to create the necessary parents.
Sorry, bit longer than planned.. I hope it helps!