Jumpstart. I have high regard for Charlie and the information that he shares with us on this Forum.
I also have high regard for information shared by Don Hyde. Don lives in Texas and is also very y-block knowledgeable. Don's recommendation shared with Felix Natoli when he was having a previously over-bored 312 again rebuilt was to not go over .040 overbore on a 312 to be used in the Southwestern part of the country. Don's reason for limiting overbore on the 312s is to avoid engine overheating tendencies in his area of the country particularly on Thunderbirds. Some of us believe that T-'Birds are more prone to overheating because of the 1 inch spacer Ford used between the timing chain cover and the water pump. The spacer was used o the 'Birds because Ford had a fit-up issue with pulley alignment, the generator, the 'Bird crankshaft damper, and Lord knows what else that I'm not aware of.
Charlie's point regarding the value of sonic testing the block has much merit, also. It is very common for the sand cores placed inside the sand mold used in the engine block casting process to shift slightly as the iron is poured into the mold and flows around the sand cores during the pouring and mold filling process. When the cores shift (move), the result can be that a cylinder wall's thickness may end up being more thin in one particular area after the bore was machined at the factory. Over-boring the cylinder for rebuilding purposes can exacerbate the wall thickness problem. When core shift is discovered prior to re-boring, it is sometimes workable for the machine shop performing the work to adjust the bore location slightly and compensate for the slight misalignment of the cylinder wall thereby equalizing the thickness of the cylinder bore wall.
Back to your inquiry. FoMoCo only supplied oversize pistons up to .040 over (3.840) for the '56-'60 y-block 312s. Aftermarket piston suppliers (examples: Sealed Power, Silv-O-Lite) still offer .020, .030, .040, and .060 oversize for the y-block 312s.
Depending upon the ridge at the top of your cylinder bores and the taper in your existing cylinders, you may only have to have the cylinders honed .010 oversize for 3.840 pistons.
Something else to consider in rebuilding your 60 year old engine block . . . Many machine shops have moved to hot water spray cleaning systems or oven baking of engine blocks and heads followed by the use of steel shot blasting systems to remove scale and corrosion before commencing rebuilding procedures. While the hot water washing systems, thermal baking, and shot blasting systems work well for exposed surfaces, water jackets in the engine blocks and heads can resist these cleaning techniques.
Talk to your machine shop, but consider turning to an over-the-road truck radiator repair shop to find hot soaking tanks that use an alkaline solution to remove metal corrosion and cooling system deposits in the engine block and cylinder heads. This method, using lye at an earlier time, was The-Way to have engine blocks and cylinder heads thoroughly cleaned to prevent cooling system overheating problems.
My suggestion would be to thoroughly de-grease the exterior and interior of the block and heads before talking to the owner or operator of the radiator shop. Remember to remove all engine block oil galley plugs and the oil filter adapter before cleaning. If the engine parts aren't completely de-greased before you present them to the radiator shop, they will likely refuse the work because the grease and dirt will contaminate their cleaning operation. After soaking, when the iron parts are removed from the hot tank alkaline solution and washed off with water, they will oxidize immediately. I supply the radiator shop with an aerosol can of GibbsBrand lubricant when I leave the engine parts to be soaked. I ask them to spray all of the exposed metal surfaces of the engine block and cylinder heads to prevent rusting of the surfaces before I pick them up.
Hope this helps!
NoShortcuts
a.k.a. Charlie Brown
near Syracuse, New York