presuming 2230m² is the
floor area and not the total area you've measured up with a 5m tape from B&Q.....
.... then you're probably only going to be cleaning about 60-80% of that actual area, depending on the type of building. Even if it is all of that area, in big open square shapes, you'll fly through it.
Commercial jobs like this... probably only 1% of that carpet needs extracting, unless there are hundreds of external doors all leading on to the carpet all over the place.
Rotary is the way, it'll give visual results and really is the only way to avoid suicide. A 60hp triple wand TM might be a feasible HWE solution, providing hoses can reach, and if you're putting that sort of kit and staff in that sort of job on a regular basis to justify having the capability (but Len runs a Titan and he says bonnet so probably best listen to him!!)
You'll probably be quoting against companies that quote as low as £0.60/m² (that's £1338 for the job). Yeah, that's life. They do a crap job for peanuts but the client's employee who arranged the cleaning probably doesn't know any better, and is earning brownie points with the boss for getting the job at such a cheap price
compared to all the other "expensive" quotes.
Good luck