This does not answer your question, but I find it relevant. You ask for uniform incomparable statements $A_\tau$ and $B_\tau$, and then ask also for monotonicity. But I claim that if one asks for the mapping on all consistent sentences, rather than just the true sentences, then we can't even get independent sentences $A_\tau$ one at a time in a uniform monotone manner. 

Kindly allow me to work over PA in place of EA. 

**Theorem.** There is no assignment $\tau\mapsto A_\tau$ mapping sentences $\tau$ in the language of arithmetic to sentences $A_\tau$ with the following properties:

1. (Independence) If PA${}+\tau$ is consistent, then so are PA${}+\tau+A_\tau$ and PA${}+\tau+\neg A_\tau$.

2. (Monotonicity) If PA${}\vdash\tau\to\sigma$ then PA${}\vdash A_\tau\to A_\sigma$. 

**Proof.** Since the trivial assertion $1=1$ is consistent with PA, it follows by the independence property that $A_{1=1}$ is independent of PA. In particular, the theory PA${}+\neg A_{1=1}$ is consistent. By the independence property applied to this statement, we see that the statement $A_{\neg A_{1=1}}$ is independent of PA${}+\neg A_{1=1}$. Thus, PA${}+\neg A_{1=1}+A_{\neg A_{1=1}}$ is consistent. The key thing to notice next is that because $\neg A_{1=1}$ provably implies $1=1$, it follows by monotonicity that we can prove in PA that $A_{\neg A_{1=1}}\to A_{1=1}$. This contradicts the previous consistency assertion. So there is no such mapping with those two principles. $\Box$

What the theorem shows at bottom is that there is no monotone version of the Rosser sentence. The Rosser sentences $\rho_\tau$ is the sentence asserting that for every proof of $\rho_\tau$ in PA${}+\tau$, there is a smaller proof of the negation. It is well known to satisfy the independence property. It follows by the theorem, therefore, that Rosser sentences do not satisfy the monotonicity property. 

Note that monotonicity is a strengthening of: 

(Uniformity) If PA${}\vdash\tau\iff\sigma$, then PA${}\vdash A_\tau\iff A_\sigma$.

I am not yet sure how to undertake the argument if we weaken monotonicity to uniformity, but I suspect a version of this will be possible. 

Note that the theorem makes no requirement on the logical complexity of $A_\tau$ or on the computability of the map $\tau\mapsto A_\tau$.

If we insist on the two properties only for sentences $\tau$ that are true (in the standard model $\mathbb{N}$), then of course $A_\tau={}$Con(PA${}+\tau$) will satisfy both the independence property and the monotonicity property.  

(And for the record, I disagree with your characterization of the examples in my paper.)