I just completed this project on my LT1045 earlier this winter.
I bought an old Craftsman mower with no mower deck or battery off of Craigslist for $50.
The owner started it for me and told me it would be a strong engine.
Installed the Briggs twin model 402707 type 013501 from it into my Cub Cadet that I purchased in 2008.
I removed the unreliable Kohler Courage that lost compression.
See my post in the New Member Forum title New Member/Winter Project for pictures.
Maybe I just got lucky but it wasn't too hard to pull off.
The Briggs shaft may have been a little shorter but it went together just fine.
I did attach one pic after the switch.
Also I removed my headlights, which i had disconnected, to allow room for the Briggs air cleaner.