The gearing will be the equivalent to having a 60t all the way down to a 32t. The chainrings will be 44t inside, driving the wheel, 38t inside, driven by the jackshaft. The sprockets on the shaft will both be 12t, the one on the engine will be a 15t. I doubt a torque converter will fit on this setup.
With most internal parts being swapped out for high performance parts, I will have a range of 1600 to 8500 rpms, with redline starting at 7500. Power band will be between 2000 and 7000, hopefully. I will need advice on how to achieve this power band. I will have an absorption muffler for noise control, as I would really like to ride this out of my apartment complex. The gearing on the cassette will be a 38t to a 15t. If there is anything you would change to optimize for all terrain, please, feel free to post here.
The sprockets you're mentioning make no mathematical sense at all. This is junior-high math.
You must know that sprockets' relationships to each other have precise values. These values, when plugged into calculators arrive at specific results.
In other words, 3 x 2 is always 6.
Do you have any idea which sprockets should drive or be driven?
I call BS on your choice of sprockets, cassette, gear ratios and rpm calculations.
Let me work the numbers you provided.
Be back with the discrepancies:
A 60t wheel sprocket has a gear ratio of 24.6:1.
A 32t sprocket has a gear ratio of 13.12:1.
These two ratios should directly relate to your custom 7-speed cassette's 38t AND its 15t gears.
There is no 15t-38t 7-speed cassette available. Ok, yours will be custom-made, right?
FWIW, 14t-34t 7-speed cassettes are readily available.
You have a mechanical disadvantage of your engine sprocket(15t) to jackshaft sprocket (12t).
12t/15t = .8:1.....
Your second jackshaft sprocket(12t) and chainring(38t) = 38/12 = 3.16:1.....
Your intermediate gear ratio is .8 x 3.16 = 2.528:1.....
Your cassette(38t) to chainring(44t) = 38/44 = .86:1.....
So your 1st gear ratio is .8 x 3.16 x .86 = 2.17:1.....
Your clutch will burn out, without your race bike moving an inch.
And THAT'S in 1st gear!
You need 24.6:1.....
Your 7th speed is (15t/44t) x 2.17 = .74:1
It should have been 13.12:1.....
If 1st gear is equivalent to a 60t, then your gear ratio is arrived by multiplying the China Girl's 4.1 gear reduction by 6:1. That 6:1 value is arrived by dividing the 60t wheel sprocket by the 10t engine sprocket (60t/10t = 6.00:1).
Multiply that 6:1 by 4.1 = 24.6:1.....
Correspondingly, a 7th speed of 32t is arrived by 32t/10t = 3.2:1.....
Multiply 3.2 by 4.1 = 13.12:1.....
HOWEVER, if you have a 1st gear equivalent to a 60t wheel sprocket, your 7th gear will NOT be equivalent to a 32t sprocket, as you claim.
Using your 44t chainring and 38t 1st gear gives you .86:1.....
To reach 24.6:1, you get 24.6 divided by .86:1 = 28.6:1, the effective intermediate gear(EIG) ratio.
So 7th gear(15t) is divided by chainring(44t), then multiplied by EIG = (15/44) x 28.6 = 9.75:1.....
9.75 divided China Girl's 4.1 gear ratio = 9.75/4.1 = 2.378:1 or 24t sprocket.
24t wheel sprocket/10t engine sprocket = 2.4:1.....
So if your 38t 1st gear is equivalent to a 60t wheel sprocket, then the 15t 7th gear will be equivalent to a 24t wheel sprocket, not 32t.