If he's planning to run it at 180F, the best (and cheapest) approach would be to use suspended-tube (with or without finned-convectors, such as
Ultra-Fin depending on what is needed) under the subfloor rather than mixing down the temp and embedding the tubing into the tile-substrate or using a plated-subfloor approach.
First order of business is to calculate the output of the section of baseboard, and make sure you have enough floor to get that much heat into the room with just a radiant floor. If the baseboard wasn't keeping up or was overheating the place, now is the time to make the adjustment. If it takes floor surface temps of 110F or something to hit the numbers you may want to add supplemental radiation such as a heated towel-rack radiator to bring the floor temp requirements down. Ideally you'd never need more than an 80F floor to heat the room, which is still pretty comfortable in bare feet. At 90F it's not going to burn but it's not super-comfortable either, at or above 105F it's downright miserable, which probably isn't the effect he's looking for.
At an average water temp of 180F 2" fin-tube puts out about 600 BTU per foot. The comfort-limit on a radiant floor is something like 30 BTU/hr per square foot, 20 BTU/hr is better) and you can't/shouldn't heat the square feet directly under the toilet. (You can under the tub, but you won't get the same amount heat transfer out of that area as under the floor.) eg: The radiant-floor equivalent of a 3' section of typical baseboard is 1800BTU/hr or 60-90 square feet of usable floor (20-30BTU/ft^2 ). The R-value of a bath-mat cuts into the heat load a bit for that ~5 square feet, but isn't a make-it-or-break-it deal.
If your peak requirements for the floor area are 15 BTU/ft^2 or so you can get there with suspended tube, but if it's 30 BTU/ft^2 the finned convector approach will still get you there. (Ultra Fin sez
41 BTU/ft^2 @ 180FAWT under a typical hardwood floor, which would be tolerable in bare feet on tile, but not exactly ideal. )
But then, most homes don't really NEED 180F AWT even on design day, and dialing back the temp at the boiler results in fuel savings, as long as it doesn't short cycle or create a boiler-destroying condensation condition. With suspended tube a boiler that is cycling on/off won't bring the surface temp much above the average of the duty-cycle- it's fairly slow reacting compared to baseboards, but it'll still keep the place warm.