Heat grill to medium (350° to 450°). In a medium bowl, whisk together honey, 2 tbsp. soy sauce, garlic, and ginger. Add steak and toss to coat. Grill pineapple and peppers with lid down until beginning to char, turning once, 3 to 6 minutes total. Transfer to a plate, core pineapple, and cut pineapple and peppers into chunks.
Whisk together lime juice, orange zest and juice, remaining 3 tbsp. soy sauce, the vinegar, chili garlic sauce, and oil in a small bowl; set dressing aside. Oil cooking grate, using tongs and a wad of oiled paper towels. Grill steak with lid down until meat is sizzling and mostly browned, turning once, 2 to 4 minutes total, being careful slices don't fall through grate.
Toss together spinach, pineapple, bell pepper, hearts of palm, avocado, steak, and dressing in a large bowl until evenly coated.