Sorry I missed your message. My memory is terrible and you probably don't need this anymore.
This post outlined the process:
http://androidforums.com/transform-ultra-all-things-root/549169-got-root-new-update.html#post4382953
These two explain what I needed to do different for Sprint:
http://androidforums.com/transform-ultra-all-things-root/517341-odin-flashing-return-stock-samsung-transform-ultra-3.html#post4402132
http://androidforums.com/transform-ultra-all-things-root/549169-got-root-new-update.html#post4402235
I used the Sprint images from here:
http://androidforums.com/transform-ultra-all-things-root/517341-odin-flashing-return-stock-samsung-transform-ultra.html#post4090294
The only part I worried about was using dd in adb to write the images to the correct partitions, people were bricking their TUs using dd to write kernels to the phone.
Hopefully you know the partition mappings, I'd have to search a bit to find them.
This post outlined the process:
http://androidforums.com/transform-ultra-all-things-root/549169-got-root-new-update.html#post4382953
These two explain what I needed to do different for Sprint:
http://androidforums.com/transform-ultra-all-things-root/517341-odin-flashing-return-stock-samsung-transform-ultra-3.html#post4402132
http://androidforums.com/transform-ultra-all-things-root/549169-got-root-new-update.html#post4402235
I used the Sprint images from here:
http://androidforums.com/transform-ultra-all-things-root/517341-odin-flashing-return-stock-samsung-transform-ultra.html#post4090294
The only part I worried about was using dd in adb to write the images to the correct partitions, people were bricking their TUs using dd to write kernels to the phone.
Hopefully you know the partition mappings, I'd have to search a bit to find them.