When I inherited my 55 Tbird, I discovered that the OEM 55 Teapot carburetor and 57 tach-drive distributor were not compatible. Gil Baumgartner (CTCI Gil's Garage) recommended that I keep the 57 distributor and replace the carburetor; that was before I learned that the Teapot carburetors can be modified to work with the 57-up distributors. 

After reading about Ted Eaton's having tested the CRT electronic distributor with favorable results, I asked him whether he would choose the 57 distributor or the CRT. He chose the CRT. The CRT Thunderbird distributor has a mechanical tach drive. It also will accommodate an electric tach as well. The CRT distributor is $240, and shipping is free. Unless you live in MA, there will be no sales tax (unless you buy off eBay). 

An expert will know that your heads, intake, carburetor, and distributor are not correct for your 56 Tbird; they won't be fooled by painting the heads and intake. Non-experts won't know the difference. 

My 56 Thunderbird is a 312 with a manual transmission and overdrive.   The engine is stock.   It was rebuilt and I assume it was bored some amount (TBD).  I plan to update the top of the engine to 57 specs with ECZ-G or 113 heads.   I'm also in the queue for a pair of Mummert aluminum heads.   I have a current version of the Blue Thunder intake manifold with the machining for a larger distributor.  My goal is to build a street 312 with a 57+ camshaft that looks stock to the untrained eye.   I would paint the BT intake and Mummert heads red to match the engine.   John Mummert suggests using 59 and later distributors vs a 57.   Ideally, I would like to use a stock looking distributor that has a mechanical tach drive that connects to the Tbird tach.   But I'm open to anything.  Thoughts appreciated!