Replacing this unit will probably be a expensive undertaking. Before doing anything I suggest you 1) make a strong solution of TSP, scrub hard, rinse well. 2) apply "gel coat" according to directions 3) use only liquid soap (NO bar soap / NO bath oils) and rinse well after every use. This should solve your cleaning issues depending on how many people use this shower.

Dimensions of room, is it the standard 5x8 ?

Most tub shower combos are 30 x 60 so you might have a problem I agree try and get the one you have clean but I will say fiberglass ones are harder to get clean than acrylic I actually use Oxyclean and dis soap to clean mine and gel gloss will put the shine and finish back on it is a days job but worth it you use the grit from the oxy to scrub away the soap film

In order to replace with a 1 piece unit the wall between the bathroom and the hall will have to be taken down (removed completely / door, studs etc.), the toilet & sink / vanity removed. There is NO other way to "slide" the new 1 piece into place. Kohler makes good 1 piece units, stick with white. This will require a carpenter / drywaller / plumber. A quality unit will run about $1400 and the lumber, drywall, paint, and labor another $5000 or more depending on where you live. If you want a cast iron tub (steel ones are crap) and tile walls you are looking at at least $8000 or more.

Or you can try my first suggestion. Not trying to be harsh...this is not a cheap or easy project. Remember, you will be without a place to bathe for at least 2 weeks.

What did you end up doing? I have the shower tub combo in my bath but it's a regular extra large cast iron tub with ceramic tile surround. I'd say my bath is 5 X 8.