First it's important to note that the twin paradox has to do with general relativity, not special relativity.

Special relativity is perfectly capable of handling the twin "paradox". General relativity is needed only when actual (physically real) gravitational fields are present. There are no such physical gravitational fields in the twin "paradox" scenario.

Taylor and Wheeler show how to determine the traveler's perspective in the twin "paradox" scenario, using only special relativity, in their example (Example 49) in their "Spacetime Physics" book, pp. 94-95. Brian Greene in his NOVA series on the "Fabric of the Cosmos" gets the same result, again using only special relativity.

It IS true that any special relativity problem can be re-formulated as an analogous general relativity problem having fictitious gravitational fields, by using the equivalence principle. When you do that, you get the same answer as is given by special relativity (and the special relativity approach doesn't have to resort to the use of artificial, fictitious gravitational fields). The only value in using the equivalence principle to convert a special relativity problem into an analogous general relativity problem is as a verification of general relativity ... it has no "value-added" in solving the special relativity problem itself, and the GR approach is more complex, cumbersome, and artificial.