Descent spectral sequence surjectivity conjecture for truncated Brown–Peterson spectra

Suppose that $d53f\langle n\rangle$ is equipped with an $\mathbb E_3$-$\mathrm{MU}$-algebra structure. Let

$$E_2(\operatorname{THH}(\mathrm{MU}))$$

and

$$E_2(\operatorname{THH}(d53f\langle n\rangle))$$

be the $E_2$-pages of the descent spectral sequences for

$$\operatorname{THH}(\mathrm{MU})\to\operatorname{THH}(\mathrm{MU}/\mathrm{MU})$$

and

$$\operatorname{THH}(d53f\langle n\rangle)\to\operatorname{THH}(d53f\langle n\rangle/\mathrm{MU}).$$

Descent spectral sequence surjectivity conjecture. The map

$$E_2^{s,t}(\mathrm{MU})\to E_2^{s,t}(d53f\langle n\rangle)$$

is surjective for $0\leq s\leq n$. This would imply degeneration of the descent spectral sequence for $\operatorname{THH}(d53f\langle n\rangle)$, given degeneration for $\operatorname{THH}(\mathrm{MU})$ and the concentration of the target in $0\leq s\leq n+1$.