Exhaust
Here's one of the most controversial engine-displacement-based conversations out there. As you've probably heard over the years, keeping the primary diameter in relation with the engine's displacement and intended usage is important. Although true to a certain extent, most of this folklore never took into consideration the Ford Windsor's need for a larger-than-usual exhaust system, or how well designed the aftermarket systems for the Mustang are.
In just about every instance we've seen or personally experienced, we find 1-5/8 shorty headers to work great. Although it cannot match the long-tube header's inherent ability to evacuate the cylinders with effective scavenging, the shorties perform admirably, fit easil, and are a lot simpler to deal with, especially if you enjoy R&R-ing your engine on a regular basis.
Once you've gone over the 6-liter area (around 383 cubic inches), consider a 1-5/8 long-tube header mandatory, and a 1-7/8 primary header as a very tight option. This is, of course, providing that you're building a healthy street/strip motor, and not some low-rpm torque monster for your tow vehicle. Another advantage of a long-tube header is that it allows you to maintain a consistent exhaust pipe diameter from the front of the car to the rear. This is because the ball flange that is used on most shorties necks down to around 2-1/4 inches, at most.
Muffler and tubing size should be at least 2.5 inches from front to back. Think about it. If you are going to continue building this car up, and are going to keep adding more hi-po parts to it, you might as well put in the best 2.5-inch exhaust system you can afford and leave it in there for the remainder of your car's life. There is no point in putting a smaller 2.25-inch system when you know that within a year, you're going to need 2.5-inch pipes. That would simply be a waste of money. Three-inch exhaust systems are cool but unnecessary for all but the most radical applications (435 inches with a blower). If you're a street guy and want to have fun with a simple stroker (like a 347 with a Vortech S-trim), 2.5-inch pipes will be more than you'll ever need. Besides, the 2.5-inch pipes fit under the car easier
Keeping Your Cool
Technically, a stroker engine shouldn't need any major cooling upgrades. If your existing radiator, water pump and hoses are in good shape, then you're ahead of the game and can spend some more money on making more horsepower. But if the car ran hot with a stock 302 in it, look into performing some cooling system mods.
Heat from an engine is directly related to the amount of friction and combustion energy it generates. An engine with a longer stroke will create more heat obviously because its pistons are traveling longer distances up and down the bores. This engine will also make more power (we hope at least) and that results in more thermal energy to press down on the piston, to heat the block and cylinder head with.
At a minimum, since the engine is out, replace the water pump with a new one, check the hoses and replace as necessary, toss in a new thermostat and pour in some fresh coolant. If you have a few hundred bucks lying around, step up to a high-capacity radiator that has more than the two cores.
If you still have extra spending money hiding in your cookie jar, go for a top-notch aluminum radiator like a Be Cool or Fluidyne unit. We've had some great result with these units in all sorts of supercharged, stroked, street-driven and even road-raced applications, and highly recommend them.
We love stroker kits and highly encourage that you build one sometime in your useful life. Although there are many things to take into consideration, the practicality and reliability of a stroked mill can bring ear-to-ear smiles. Again, we'd like to emphasize the importance of properly accessorizing your stroker motor.
What you'd want is to take full advantage of all the additional cubic inches in order to make more power. After all, isn't that the point of all this hard work?