I'll agree with the transition curves. With two feet of straight track, you can easily use 12-inch long transitions at both ends, and still have close to 12 inches of straight track. The key is that, normally, half the length of the transition is in what was the circular curve, and have in the straight between them.
Note that, to keep the curve centers and radii the same, the straight section between the transitions will NOT be on the original alignment. The transitions will have to start a little earlier, and the straight will be at a slight angle, in order to keep the original curve locations.
If you have printed transition templates, showing where they meet straight and various radii track, you can splice together a combination template, and play with it to get the exact alignment you need.
Another trick is an "artist's spline", a long length of flexible wood, for drawing smooth curves. You can pin both ends along the curves, and allow the middle to adopt a natural transition between them - that's what it's for. For this, you'll need one about six feet long. A length of any flexible, springy material will do, as long as it curves, rather than kinks, when bent. Two pieces of code 80, or heavier, rail, soldered together, might work.