Anyone know why that might be? is theoretical work shifting toward the lambda calculus as the preferred method to describe results in computation?

Because lambdas/TMs are all equivalent it doesn't really matter which description you use. In most computability work, instead of saying "consider the TM which computes f" or "consider the lambda function which computes f, writers will often just say "the computable function f".

Also does anyone know of applications or even just potential applications of the Recursion theorem, not already mentioned in the wiki?

You can prove Rice's theorem with the Recursion theorem.

You can use the recursion theorem to reduce Wang Tiling to Halting Problem. A combination of recursion/s-m-n can be used to prove a lot of reductions in this way.

Finally, what academic journals would have related or similar results to the Recursion theorem?

If you want to dig deeper, another common technique seen in computability theory is the priority argument and its generalisation, the injury argument (this is like a computability version of forcing in set theory).

The arithmetical hierarchy is another important mainstay and has a deep connection to computability (this is Post's theorem).

Neither these really have much to do with the Recursion theorem, but they're important topics in computability and possibly what you'd look at after learning the Recursion theorem/index sets.