Car Service - Kawaguchiko to Fuji 5th Station?

Hi all! I have an upcoming trip to Japan and one of my goals is to summit Fuji. I’ve done fairly extensive research on the Yoshida trail and am aiming to do the ascent and descent in the same day as our itinerary doesn’t easily allow for more time than that. That being said to maximize our chances of getting to the summit safely I’m trying to find options for getting up to the 5th station earlier in the day. The buses get there at 7:30am, and with an hour at the 5th station to acclimate we would be left with approx 10 hours to get up and back down to the last bus. Taxis normally start around 6 and we’ve been told you could try to book a taxi earlier but it’s not a guarantee you’ll be able to. Does anyone have experience with, or know of a car service for hire in Kawaguchiko that we could hire to get us up to the 5th station earliwr than the busses? Thanks!