Calm down. You haven't been ttc long enough for 50% of people trying for the same length of time to have fallen pregnant. 80% of totally healthy couples will conceive in a year. 90% within two years.
Adding progesterone has not been proven to extend luteal phase. Short af is generally not a problem.
Start with the b6 and see if that helps over the next few cycles.
The nhs doesn't have a magic solution to 'hormonal imbalances'.
Getting blood tests won't make you pregnant... it just wont. Extensive testing so early in your journey won't help you. It just won't. Even if an issue IS found, you won't get funding for ivf treatment until you are proven to be infertile (which is ttc for a year or more without clinical pregnancies) and ttc for at least two years (in some areas it's 3).
I get the impatience, I do. But I don't think this is the way to improve your mental health about ttc. It's totally normal to worry about things, but you're going to turn this natural worry into health anxiety. You're medicalising something that is highly unlikely to need to be medicalised at this point.
Why not look at b6? Why not do something helpful for yourself, like evaluate your diet and exercise? Even if you're in the 'normal' bmi range, studies show the 'optimal bmi' for conception is 21-22.
Go back to the gp at 12-18 months ttc. You're unlikely to not be pregnant by that point, which is why that's what recommended.