Does Strionic Resonator copy triggered abilities that trigger during the upkeep step before the controller receives priority?

Strionic Resonator's activated ability reads: '{2}, {T}: Copy target triggered ability you control. You may choose new targets for the copy.' It can target any triggered ability on the stack that you control, regardless of when during the turn that ability triggered (CR 112.3, 603.1).

Triggered abilities that trigger during the upkeep step — such as 'At the beginning of your upkeep, do X' — are placed on the stack after they trigger (CR 603.3). Once they are on the stack and players receive priority, you can activate Strionic Resonator to target and copy them (CR 116.3, 603.6).

The key point is that triggered abilities don't resolve immediately when they trigger. They are put on the stack, then players receive priority before anything resolves. This window is exactly when you activate Strionic Resonator (CR 116.1, 603.4).

Concrete example: You control Howling Mine (triggers at the beginning of each player's upkeep) and Strionic Resonator. At the start of your upkeep, Howling Mine's triggered ability goes on the stack. Once you receive priority, you pay {2} and tap Strionic Resonator to copy the triggered ability, causing each player to draw an additional card — so each player draws two extra cards total.

Note that you must control the triggered ability to target it with Strionic Resonator. If an opponent's triggered ability goes on the stack during your upkeep, you cannot copy it with Strionic Resonator (CR 602.2).