I've read the OP's post at least 5 or 6 times and still can't quite get what he is asking.
Is he asking if he can he swap a 8.1 into his 02 1500?
Is he asking if he can swap a 5.3 in place of the 8.1 in a different vehicle?
The answer to both is yes.
If you are swapping a 8.1 into your 1500 to replace the 5.3 you will need to get the ECM and trans from the 8.1 donor, preferably a 2500 Suburban/Yukon XL/Avalanche, or van. The burb chassis 2500 already has the ECM, 4l80/85 trans and can have whatever transfer case you already have on your suburban, or it already has mounted up to swap over. That includes the better hydroboost brake master cylinder and engine mounts. The van 8.1 also has the 4l80/85 behind it, but different transfer cases. If you keep your transfer case from your 1500 you will need to change the input gear to work with the 4l80/85 output shaft, which has different spline counts than the 4l60/65. The 4l80 is longer than the 4l60, so you will also need the transmission rear mount and cross member and will need to fab them in.
The 4l60/65 in the 1500 can't survive very long at all behind the 8.1. Heck the 4l60/65 barely survives with stock power and torque behind the 5.3. The 8.1 makes more torque right off idle than the 5.3 makes at peak. Though it bolts right up.
You will also need to think about upgrading the front suspension for the heavier powerplant if you take this on. Honestly, if you had a wrecked 2500 with a solid 1500 to play swap bits I would move the cab over from the 1500 to the 2500.
If you are going to swap in a 5.3 into the 8.1's place in a 2500 chassis, why? The 5.3 can't tow or work like the 8.1 can. The 8.1 has over 300ftlbs of torque, right off idle, rises linearly to 455+ and stays there until it shifts. On paper they have similar HP, but the area under the curve, not the peak to peak, is where it makes all the difference. The only acceptable swaps away from the 8.1 would be a 6BT or a duramax.
Now, if your 8.1 donor is a truck with an allison or ZF-6, you will need even more parts to make this work. The trucks have a factory 2 in body lift to clear the allison or ZF-6, and will not fit unless you lift the burb cab 3 in. I know it seems weird, but the burb cab sits 1in lower than the normal truck cab, so you have to make up the 1, then add 2 more to clear it. If you have a ZF-6 donor, let me know.
The most common swap is the entire front powerplant/trans/hydroboost into a square body 1500 using the 4l80. There is a 8.1 swap facebook group with tons of how tos, the part numbers for swap parts etc.
The holy grail would be the 8.1 with the 6 speed allison, only available for 2 years, but you need so much chassis parts and reinforcing it would be easier to swap your cab over.
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