I was a mobile home installer several years ago. You said manufactured home, so not a modular. You have two steel rails running the length of the house. Those sit on block pillars. Depending on the home brand, the distance between those rails will vary. Probably 96 inches, depending on the brand and the spacing between the piers, which is typically eight feet. Hopefully, your tank will sit across the joists, not parallel to them. That said, the tank will be near the rails or the exterior walls so that the weight is distributed relatively evenly. You said it was on a permanent foundation, but it's most likely sitting on piers with a brick or block skirt. If that is the case, it carries no weight. Either way, I would go under the home and place some crawl space jacks with 4x4s to spread the load. I would put those under the tank and not try to do the complete room. Be sure to get some support under the exterior edge of the house, as that will be the weakest area. You can use jacks or build piers from 8-inch dry-stack blocks and a handful of wedges from Home Depot to tighten them. If you have any questions, please ask. Also, you might ask the installer if they will build you some piers where they need to be while they are under there working anyway. They have the block, wedges, and the know-how. You are probably looking to give up a six-pack of cold beer to make that happen.