You can have factory new, factory remanufactured, factory overhauled or field overhauled. Factory new and reman come with zero timed log books factory or field o/h do not. Factory reman or o/h must naturally be done at the Lycoming etc factories. FWIW there were only 2 shops who i would let go anywhere near my donks for overhaul 1. Roger Verney (Scone Aircraft Maintenance) and 2. BAE at Archerfield. OHC cylinders are false economy and i recommend Factory new cylinders being fitted. Check the AD's on ECI, Millenium etc cylinders. They're having problems with cracking etc. Check the WRITTEN warranties thoroughly, and confirm what is going to be replaced or bought back to OHC. Personally I like to have my engines worked on in leu of exchange. I hope this helps.
I am not sure if Roger is still working, he may have come to his senses and finally retired, like i did.