I would urge you to be really careful with jet tubs. I have had nothing but problems with my Bain Ultra jet tub. My tub would turn on randomly throughout the night, so I would be in bed and hear air rushing from the tub in the middle of the night. Within a year of installation the lights on the keypad stopped functioning. Called their customer service department and they will not honor their warranty. Apparently their electronics and keypads are poorly constructed. The Bain employee I spoke to suggested I replace the tub altogether.

A 60" tub is small (that's standard alcove tub size), but you may have room for a 66" if the filler does not need to go on the end. Check out Signature Hardware, Maxx Tubs, in addition to the V&A leemiller suggested. Pay careful attention to the specs in terms of the inside bottom dimensions. I have tried many freestanding tubs on display that I though were pretty uncomfortable. If you have anyplace where you can go sit in the tubs on display, it might help you to figure out whats best for you. Good luck with your search!

What thickness is your subfloor? Do you have a flooring elevation in another room that you'd like to match, example, the bathroom floor to the hallway or bedroom floor at the bathroom door threshold? I do recommend waterproofing the floor with a free standing tub. If you did use cement board, you need to bed the cement board to the subfloor with thinset and then fasten it with screws of nails. The purpose of the thinset is not to bond the cement board to the floor. It's to fill the gap between the two so there is no up and down movement that can lead to grout and tile failure down the road. The thinset is not optional, it's required. If your current subfloor is adequate, I'd recommend you go a step beyond cement board and use something like Ditra membrane. Ditra is only 1/8" thick and it has a waffle structure. The structure is designed to isolate the tile bond from any subfloor movement, so you'll get a better performing floor. Ditra comes in 39" wide rolls, it's available at the box stores. If you cover the seam between adjacent sheets of Ditra with Kerdi-Band or even strips of regular Kerdi, you'll have a waterproof floor. If your tile is a small mosaic, Ditra has restrictions regarding tile less than two inches, so you could use another membrane like Nobel. If your current subfloor is inadequate, I'd recommend adding 3/8" or 1/2" ply underlayment over the subfloor, then Ditra. Half-inch ply will provide added strength to the floor to reduce deflection. Half-inch cement board offers no additional strength whatsoever, cement board is simply a transitional material to get from wood to tile. The Ditra (or another thin membrane) is thin enough at 1/8" to not add excess height to the floor, but it's also an excellent intermediary between plywood and tile. And it'll give you better performance than cement board and a waterproof floor as well. Yes, I'd tile the entire floor and place the tub on the tile.

I'm trying to think of the brand that sells a mounting block similar to what your plumber is talking about. It's not coming to mind - but you would be able to put it behind the tub and never know its there (depending on the angle of the tub) The other option would be having a small wall built behind or at the end of the tub to house the valve - you could also make this a shelf feature for candles or bath products etc.