Zoysia from seed is not a very successful endauver. Even if you get good germination it will take 2 or 3 years to be a nice healthy lawn. Throw in shade and you will even have a smaller chance things work out.

 

Trying to do bermuda or zoysia from seed is a recipe for failure.....buy sod, shred it and sprig it.

 

It's much cheaper to seed. Blackjack cost $100 to seed 5K (10 lbs of seed). If you seed it in early summer it germinates in under a week and you have a full yard in less than a month. Sprigging only makes sense for people who have irrigation and/or can afford professional delivery/installation. Not everyone has the tools to sprig. Lastly sod is the most expensive. $100 vs. $4,000+

Before (mostly goosegrass which I killed):

After (1 month later):

Before (After I killed and raked the yard, yard was salad before):

After (1 month later, still some weed pressure)

 

Your grass will do fine without all of the humic and carbon products. There's some evidence of rooting benefits with those products but the results are not consistent and they haven't demonstrated much improvement in turf quality when you read the studies. Just get the cheapest form of nitrogen you can find (urea or AMS), both will last at least 6 weeks in turf (ignore the marketing about fast and slow release fertilizers). If you want to learn more, check out Dr. Travis Shaddox on Youtube (Channel: Turf Epistemology).

I don't recommend mixing Bermuda and Zoysia though. Zoysia needs way less nitrogen and is a bit more finicky (slow to recover from damage, susceptible to fungus). It does better in low light situations (partial shade [4 hrs] to partial sun [6 hrs]) and has less weed pressure when established but it'll never thrive in shaded regions either. If you're getting 6-7 hours, that's enough to grow Bermuda or Zoysia to acceptable levels. Any less than 6 hours and I'd recommend Zoysia or opening up the canopy a little more. Once your grass is established, you can put the grass on PGR starting next spring or at least 3-6 months after seeding (helps with turf quality in shaded areas, and rooting) and it should do ok with at least 6 hours of sunlight and a higher height of cut (no less than 1", up to 2"). You may want to buy a $30 light meter on Amazon and measure the amount of light your back gets in the most shaded parts to make sure it's at least in the partial sun range (4-6 hours of sun). Any less than 6 hours and Bermuda will germinate, thrive for a few months then quickly die. Any less than 4 hours and zoysia will never be happy nor your yard full.

There's always mondo grass or other shade happy ground covers if you simply cannot get enough light.
You don't have to sod or sprig. Yes, they will produce a higher quality lawn than a seeded lawn, but it's still not as cheap as $100-$200 of seed and a bit of elbow grease (weeding and dealing with problems). If Ron Henry can do it, so can you ...just don't buy any of the products he's trying to sell you.

My backyard seeded with blackjack ( 1 month after seeding) which only gets 4-6 hours of sunlight except in the center hence why it died in the first place>

We really need to cut down some trees but there's others on the neighboring properties as well so it's pointless. I could always try KBG or a shade mix and overseed each year but I hate cool season grasses and they'll die back each summer in this Texas heat.

 

Honestly, this is probably the most helpful to you to get an idea on the differences between Bermuda and Zoysia, as well as how PGR helps them with turf quality.

https://www.usga.org/content/usga/home-page/course-care/green-section-record/59/16/how-much-light-is-enough--daily-light-integral-requirements-for-.html

Dr Shaddox did a show about a shade study done on biostimulants, PGR, iron sulfate, propicanozole etc which may help you as well.

 

. My CEC is low, but I am, and will continue to, add Lesco Carbon Pro-G, Humic DG and several N-Ext products on a regular basis this year to keep moving that in the right direction.

If money is a factor, you could save a lot of money by not applying these products.

My CEC is pretty low at under 4 and my lawn looks pretty good. Those products mentioned above are good, but are not cheap. You can get fantastic results by using cheaper N sources such as Urea or AMS.

I only mention this because you said cost is a factor.

 

Why would you join a forum like this in an effort to get advice under "anonymous" user name? Looks like a bot post to me.