CR461:
"You have to spend all the actions of an activity at once to gain its effects. In an encounter, this means you must complete it during your turn. If an activity gets interrupted or disrupted in an encounter, you lose all the actions you committed to it."
CR279: "If an item takes 2 or more actions to reload, the GM determines whether they must be performed together as an activity, or you can spend some of those actions during one turn and the rest during your next turn."
So, the GM determines if it requires:
A) 2 separate reload actions, or
B) A single 2-action reload activity
If it is A, you can freely use Running Reload, or reload across turns.
If it is B, then you must spend two actions (as an activity) together.