Bradford–Ionascu conjecture for unit fractions in Gaussian integers

Let ${\mathcal E}:=\{0,1,i,1+i\}$. For $n\in\mathbb{Z}[i]\backslash{\mathcal E}$ whose real and imaginary parts are nonnegative, consider decompositions of the form

$$\frac{4}{n}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}.$$

Bradford–Ionascu conjecture. Such a decomposition exists with $a,b,c\in\mathbb{Z}[i]$ such that the real and imaginary parts of each of $a$, $b$, and $c$ are either both nonnegative or both nonpositive. This is the Gaussian-integer analogue of the Erdős–Straus conjecture, with the cone restriction reflecting the positive cone generated by the basis $\{1,i\}$.