First, I must need a new computer screen because I can't SEE any original paint left on that frame. Maybe a trace of the head scallop? A Saw-z-all is a great tool, but it needs to be in the last resort tool box, not the first tool you grab. It might not help you at all, but for others that encounter rusted parts, first try some of these ideas. It would have been nice to have saved that 12" tall "forged top" Wald goose neck. You could have sold it to a Cycle Truck guy or traded for parts.
Soak the problem parts with penetrating oil. Lots of oil concoctions have been discussed on the CABE recently, my guess is most of them will work, not much Majic here. Remember, parts have two sides, soak the seat post from both the top, and then also from the bottom after the crank was removed. Same with the stem, top first, then from the bottom after you remove the fender bolt.
You need some vibration to break up the rust. I use a good sized brass hammer. It's an exercise in patience, and repetition, NOT how big is your hammer, or how hard you hit it. You only need to tap it, not beat the crap out of it. In the case of the fork, hold one leg and tap the hammer on the steer tube. You will be able to hear where it's loose and hollow, and where it's rusted solid. Hit the rusted solid area for a while, work all around the area on all sides. Place some more oil and let it sit a day or two and repeat. Eventually, it will loosen it grip and you will save a fork. Same with the stuck seat post in your frame. I have no doubt you will be able to remove the seat post, but saving your original paint is doubtful.
Using heat works, but let's keep it in our tools of "last resort" tool box.
It took 50 to 60 years for all that rust to form, you need to be patient, and persistent to break it back down.
John