Keying + Tracking onto Tablet/Smartphone with Green Screen Display in Adobe Premiere or After Effects
Trackers never hurt and there's almost no reason not to use them, but there's no substitute for pre-production and field testing. The only failure is failure to plan.

Ideally your markers would be high contrast, however you can place darker green markers on a green screen which can be entirely keyed out if the artist doesn't need them, but will still be useful if they are needed.

Since you've already shot this without markers, your best hope is a three-point tracker that can find and hold the screen edges. Since you say you have minimal motion, this shouldn't be too hard.