Here is a simple (the simplest?) setup that considers both cases you highlight.
Consider a simple model in which orders o_i arrive with a constant rate of \lambda and signals s_i arrive with a constant rate of \eta. There is a batch-auction design, similar to Ethereum L1, with a slot length of l. Searchers compete strategically for transaction inclusion and MEV-gains, WLOG we look at the simple case of two searchers and define the latency advantage of the fast-searcher A vs slow-searcher B as x. Each order represents a MEV opportunity and searchers can submit one or more transactions t_i=(t_{i1}, ..., t_{ik}) with associated inclusion bids b_i=(b_{i1}, ..., b_{ik}) to take advantage of it. For now, we consider the simplest case in which MEV is extracted with only one blockchain transaction (k=1).
Gains
Searchers compete for orders that come in the initial interval of length l-x, while in the last x milliseconds only A can respond to orders and signals. Note that in this design searchers can also change their bids for previously submitted transactions, so in the last x milliseconds A is the only one that can send new transactions to take advantage of new orders (write monopoly) and change past bids to take advantage of new signals (rewrite monopoly). Note that this also entails canceling transaction by setting a bid of 0 for example.
Searcher A gain-advantage depends critically on batch-length and latency advantage
g_A(x,l) - g_B(x,l) = \underbrace{x\lambda v}_\text{write gain} + \underbrace{x\eta(l-x)\lambda |v-b_B|}_\text{rewrite gain}
Note that we have assumed for simplicity that: (i) the opportunities are copies of the same order, (ii) all the signals received give a proportional informational advantage over order being rewritten. So it is really the best case for A, but as you can see it is still at most linear in x (the rewrite term is actually sublinear).
Some directions that would be interesting to explore: quantify informational advantage and valuation update rule instead of using true value & do a more realistic model with different types of MEV-opportunities and different information structure of signals.