Cost of swapping a 10 to a 13 speed.

Why would the rears need changed out?
The only thing you will need to do is shorten the driveshaft and have the ecm reprogrammed to match the transmission.

 

True that. Generally a ten and thirteen speed has the exact same final ratios.
They can be different, so you would have to confirm the model numbers.

 

It probably won't be cheap. They probably won't accept your 10 speed as a core for the 13 speed.

 

You can convert a 9 speed to a 13 speed but not a 10. To convert a 10 to a 13 requires a whole new transmission. They will charge a core charge when you purchase the 13.

 

They are actually off by .01 but that's such a small amount you wouldn't even notice it in your speedometer.

 

If you go to a small independent shop they will likely accept your good 10 as a core for a rebuilt 13. On my last truck i got quoted 2500
installed with my 10 as a core. That price was just the labor and transmission, did not include the machine ship costs for shortening the drive shaft or the part costs for a new clutch.