I have around 100 3x3” travertine tiles in my growout tank and I haven’t experienced the same issue you describe with algae. Why do you expect them to leach iron? Untreated natural travertine should just be made of limestone.The best tiles are from this company in Wisconsin called Alternative Reef. They are thin, fired ceramic tiles and don’t leach anything. They are slightly convex so they kind of sit on their corners giving just enough space underneath for pods (if I turn one upside down, it’s coated with pods). They are thin and easy to bandsaw. If there is interest I can try to pool an order together.
I’ve tried 4” Home Depot travertine tiles but they leach something (probably iron as you would expect from travertine) that makes green algae grow a little more enthusiastically on them. And they aren’t uniformly smooth, and they are impractically thick for sawing up encrusters. But look natural and could work ok for acros or euphyllia.