Midwest Aircraft Services Inc. - Aircraft Repairs Newton KS has done great work for me and many others I know around the Wichita, KS area. They are experts with some of the big & complicated Lycoming engines and get those in from all over the country.
Barret Precision Engines in Tulsa is also good... I used them for my overhaul but more as a subcontractor. I intended to assemble my engine under supervision to gain that experience, but my plan got derailed and I was left in a pickle after getting everything back from Barret, Divco, Aircraft Specialties, Firewall Forward, etc. Midwest was willing to take all of my parts (with tags/records) and assemble them into a functioning engine and sign it off, fortunately.
I chose to spec my own overhaul so I could get the "extras" done such as the Centrilube Cam mod from Firewall Forward, along with precision balancing from Barrett for the rotating components AND flow-matched cylinders. Those were my first-run jugs that they overhauled. After a break-in and dynamic prop balance, we got it down to 0.01 IPS and it feels like a sewing machine instead of a lumpy 4-banger. I was also confident my crank, case, jugs, etc. were good, otherwise I might have considered a factory option.
Powermasters in Tulsa has a stellar reputation on Beechtalk, and I know of some Mooney owners that have used them as well. They're experts with the big Continental engines, but I think they can work their magic with Lycomings as well.