The above new perspective allows us to compare different design choices.
Design choice 1: A new block of height (m+1)c triggers an entropy-injection event where m is a non-negative integer and c is relatively large. The entropy is from its ancestor block of height m c. The injection time is t_{mc} + T, where t_{mc} is the time slot the ancestor block is produced. If t_{mc} + T \le t_{(m+1)c}, we give up this injection opportunity.
Discussion: The growth rate of the honest block tree is still at least \lambda_h \frac{1}{1 + \lambda_h \Delta} (because honest farmers will not take advantage of entropy injection at all). The growth rate of the private block tree is still at most \phi_c \lambda_a (because we may lose some injection opportunities). Also, the adversary cannot go back in time.
Design choice 2: A new block of height mc triggers an entropy-injection event where m is a non-negative integer and c is relatively large. The entropy is simply from this new block. The injection time is t_{mc} + T, where t_{mc} is the time slot this new block is produced. Here, T is relatively large.
I feel that a very similar discussion applies here. I will double check.