I am currently reviewing a paper for a journal (area of ecology, organism-environment interactions at various spatiotemporal scales, so including macroecology and evolutionary ecology). Now I am doing a second review of this paper (after resubmission). They submitted a valuable manuscript, but they ran into challenges which are quite difficult to solve. In particular, their statistical population models didn't converge properly; the models would need at least 10x, preferably 20x or 50x as much iterations to run, but they are very slow - taking 2 weeks to run already. I already investigated a bit and found an approach which would make the models run 1000x faster - this would solve the issue. I don't think this approach has been used yet (currently investigating this).
I am about to give them very detailed instructions on how to implement this approach in their models. I am not an experienced reviewer (this is my first paper to review), but (1) I think this is a bit beyond the usual work done by the reviewers? It is also possible that this work will be very challenging for them, since not every biologist is skilled with models and it's much easier for me since I am a specialist in development of new population models. So, (2) is it appropriate for me to offer them cooperation on their paper, with the possibility of becoming a co-author? (3) Should I ask for co-authorship for this? Or, is it better to just contribute and wait if they offer co-authorship to me? If this happens then the editor would probably need to find another reviewer instead of me for the next revision, because of conflicts of interest.
(The review is currently double blinded, so I don't know their names, but I signed the first review and offered my email already, so they know mine.)