That is the life of a designer. They are involved in pre-production mostly (bigger studios employ them throughout production). Developer is also a good term you have there.
But this is for the idea as to what you’re saying. If you need someone to make the core mechanics of the game, in engine, then you want an engineer instead. Probably called a gameplay programmer or systems engineer, depending on the kind of game (like fps vs puzzler for example).
Generalists may also work as a better long term fit. This sounds like what you are, and every generalist has general skills under multiple disciplines. They can fill most roles if the need be while having strengths with specific responsibilities. Its a per basis thing though.