I have a 64 Lincoln Continental convertible and it is fully custom. I am trying to do something with the 430 that would give it some extra horsepower and torque. I do not want to swap engines, just add some extra power. Can anyone give me advice? Does anyone make performance parts for this engine? Can you bore it out? What transmission would I use? Help!!!

You have a heavy custom car. Your options are limited. I would not recommend spending big bucks on custom pistons, head porting, nitrous, stuff like that.
Holley makes a replacement carb that is easy to jet properly, but depending on what you have, a carb change may not be necessary. Carter carbs can be tuned for perfomance too.
The engine would need a modest cam change, have your cam reground for torque and not high RPM horse power. Take your time here, do your research on the cam profile you want. Too much cam and everything vacum will not work right. Oregon cams does this, about 150 bucks. They have done two for me.
Go to electronic ignition, several brands available.
Open up the exhaust, 2 1/2 or 3 inch pipes from manifolds back to your preference of mufflers. Flowmasters-whatever tone you like. A full length exhaust will still flow well and keep the noise behind the car. Spend some money here at a good shop.
The transmission will be a problem. 430 engine for those years have a bellhousing bolt pattern that a C-6 will not bolt up too and I do not know if a C-6, if adadpted to fit the engine will fit the chassis. From personal experiance, the stock transmission is weak and a 2000 stall convertor must be custom made. expensive. The trans can be beefed up a little, but I lost high gear several times. Just blew clutchs out. Not a trans made for high power applications. Maybe someone else knows of a solution to the weak trans. Good luck. TJR

Something to consider. Buy the stock cam on ebay and send it out for regrind. Same with carb, if you have Carter set up. minimizes down time when you can get all the replacement parts before you do the teardown.