Word length using entropy : Maximum entropy criteria
Disclaimer: This is based on generic information theory knowledge only. Too long for a comment.

Summary: The pointwise product of your two plots should go to some limit, as the relevant blocklengths and sequence lengths increase. 

I don't know if this applies to DNA but in theory if your sequence is ergodic (stationary, and time averages are the same as ensemble averages, for long enough sequences) then the two entropies are related intimately.

The whole point is, if you obtain a "block" entropy $H(X_1,\ldots,X_n)$ for a block of length $n,$ then
$$
\lim_{n\rightarrow\infty} \frac{H(X_1,\ldots,X_n)}{n}=H_0
$$
which is the entropy per symbol, i.e., the entropy rate, what you call shannon entropy as opposed to block entropy.

Now, the question of estimating these is a different question. In fact your program does this by a sliding window technique, which then means that it is averaging overlapping thus dependent samples.

Define the shorthand $X_i^j=(X_i,X_{i+1},\ldots,X_{j})$ where $j\geq i.$ I am sure that under suitable conditions an estimator of the form
$$
\frac{\sum_{k=1}^{n-\ell+1}\hat{H}(X_k^{k+\ell-1})}{n-\ell+1}
$$
where $\hat{H}(X_k^{k+\ell-1})$ is a suitable estimator for block entropy, will converge to a multiple of the entropy rate, i.e., to $\ell \times f$ where $f$ is a correction factor. However, one may need to let $\ell$ grow with $n.$