Your best bet would be to retain a structural engineer to review and design what you wish to accomplish. Second guessing might lead to problems. For example, the suggested concrete and reinforced concrete would create a mass that, if not anchored and designed properly, could lead to that mass swaying improperly under load, causing structural damage. (Seismic engineers know this all too well.)

Construction means, methods, and materials can all have complicated interactions depending are how, where and when they are used. Plus, you have building code regulations to address. Answer: There is no easy or definitive answer owed to the presently known and unknown values you wish to design around.

We used an engineer when the addition was planned to correctly assess the foundation requirements with the 2nd floor laundry in mind- I know we exceed minimum code requirements by a long shot. I guess the actual construction of the second floor laundry room, he left up to the contractor.

I have the impression that many people retro-fit existing second floor areas, particularly closets, to make room for laundry rooms. What do they do in the absence of an engineering report?

Surprised your engineer didn't do the 2nd floor too. However, you can use engineered-wood joist, or add sister joists (effectively doubling-up a floor joist). Since you are using a FL washer your movement will be side-to-side and you should take into consideration a worst case scenario (washer goes into spin and is completely unbalanced due to a washer fault). Try to design the flooring to drain without having have a curb, if possible. This is just for reference as it utilizes a pan: Avoiding a Laundry Room Flood in an Upstairs Laundry Room

Have you considered steel beams under the laundry room floor, and have them run under the machines and parallel to the wall to which the machines will back up. If the steel beams are too pricey, perhaps a good load-bearing wall under the area where the machines will sit? You really want to avoid the "trampoline effect."

Extra layer of 6/8" plywood (not particleboard) sub-floor perpendicular to grain of first layer might help, too. I suggest avoiding particleboard in case of a flood (not to mention the formaldehyde outgassing potential) .... p'board will swell and possibly crumble, too, if gotten wet from a washing machine hose blowing, or any sort of disaster. A really good grade of plywood, like ADX, should not. It's expensive, but you're looking at a small area.

Drain in floor is a good idea, too.