I’ve never heard of Murphy’s Oil. Does it make the hardwood slippery when it’s applied to the floor? I can imagine my son having a blast slipping and sliding all over the floor once I cleaned it 
I actually have the original H20 mop. And it cleans the grout really well too. Give it a shot! I bought mine on sale for $50, so you might wanna wait until you can get it at a good price. Regular price is around the $90 mark, which is a bit pricey for me