The code in "How to factor 2048 bit RSA integers with less than a million noisy qubits" assumes a cycle time of 1 microsecond, which is too strict for neutral atoms. 1 millisecond sounds about right for neutral atoms.
How much do the resources in "How to factor 2048 bit RSA integers with less than a million noisy qubits", that is, Shor's algorithm on the Surface code with Lattice surgery, not transversal gates blow up when neutral atom cycle times are assumed?
The simplest conversion is just scale the time. The cycle time increases by a factor of 1000, so it takes a decade to run instead of a week.
A much better conversion is to account for the switch from lattice surgery gates to transversal gates. You would expect this to reduce the 1000x overhead to somewhere between 100x and 10x. For example, in "Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays", they show that my 2019 factoring circuit could run in 5 days (instead of 8 hours) when ported to a neutral atom architecture.
However, there's a catch: magic state production. Magic state cultivation doesn't benefit from transversal gates. To run new 1M-qubit-count factoring circuit, which has even more Toffolis, they'd still need ~10M qubits doing distillation for a ~week. Reducing the amount of distillation, so it actually fit into 1M qubits, would make it take months or years to produce the needed magic states on a neutral atom machine.
Neutral atom estimates in 2025 feel a lot like superconducting estimates did in 2012. The costs are dominated, in both space and time, by magic state production.
