Why 1939 limited American leverage in a naval crisis

Could Roosevelt have acted as an effective peace broker in a 1939 naval war?

Probably not decisively: none of the three major naval powers was strong enough to prevent the other two from fighting.

American naval power in 1939 was too weak to compel the other major naval powers to make peace. In this reading of the balance, the third power could watch two rivals exhaust one another or enter to influence the outcome. It could not simply impose a settlement. Isolationist pressure before the 1940 election further limited Roosevelt's freedom to act as a mediator. Diplomatic ambition still depended on enough force to make other governments accept mediation.