IIWY, I'd take the monorail to Hamamatsucho (last stop) and a cab from there. That will cost you a fraction of the limo.

If you just can't stand the thought of public transport, then you could get a cab or an Uber car for probably two thirds of the limo prices quoted by the site you linked to. Some of the regulars here may well know what Uber charges for that trip.

If you really have to have a limo, I would prefer MK (as cited in the post above) to Hinomaru (the parent company of the page you linked to). This is purely on the basis of the experiences I've had in the regular taxis run by both firms. MK tends to be a cut above the others.