I contacted Stanley Steamer 800# to see about carpet and tile services. They explained what they would be able to do, especially with the tile.
They claimed the high pressure vacuum would make the tile grout next to white. In the end, they put on a pre-treatment, scrubbed the grout lines with a brush and vacuumed up the water, but not with anything special, just a circulating brush that had no more power than my washer.
I was promised a deep clean and got a deep price with no visible improvement. I've hand washed the carpets myself with better results.
Monetary Loss: $539.