Are you unhappy with the Floormate results?
I used to use hot water and liquid Spic and Span, or Top Jog, or ammonia. I no longer have any linoleum, except under the washer/dryer. I also have numerous Hoover Steam mops.
Armstrong makes a wonderful solution called "One and Done". It mixes with water. I loved the way it cleaned vinyl flooring above all other chemicals, really.