Try the iron, it should work on small spots. I've used this method before and the iron just lifts the wax into the towel. Once you get the actual wax up, then you can work on any stains left over from the wax color. I

Paint thinner is the remover for wax build up.

A stone floor can be ground down and resealed. This is something you can look into. Feel free to reach out to a stone refinishing professional (anyone who lays marble or slate) and get them in there to do a deep clean. Let's figure out how much needs to be done to these stones before grabbing your chisel. Once the stones have had their deep cleaning (and the mortar/grout lines) you can then reassess. If they need grinding/polishing, then go ahead and have that done. That's the beauty of these long-wearing floors. They can be refinished and refreshed for decades. They should out last several homeowners.

Were you instructed to purchase all 4 cleaning and maintenance products??? You would do very well to have the refinisher come in and (purchase all products from him/her) show you how to maintain your floors. You will probably pay $50/hour for this 1-2 hour tutorial. You and the refinisher will work these spots together and apply the finish oil to bring back the original look. And then you will learn your weekly, monthly and yearly maintenance requirements for an oiled floor. As pretty as these floors are, they take work. Much more work than a polyfinished floor.