Hey @cjwm97 welcome to the forums - in the kit you linked, you're right that the mount for the deck at the top of your dash, above the vents, would be wrong for a RHD car, but the kit also comes with a sort of trapezoid shaped fascia that is designed to fit down in the lowest position in the console, just above the transmission tunnel, which is where a lot of older 240s mount the stereo.
To put it in the top position I think you'd just need to make your own or modify the stock bracket.
In terms of keeping the thing mounted steady, generally you lock the mounting cage in place by pushing out a bunch of tabs, and it is then locked in the fascia plate, and the fascia is screwed to the dash. If you needed it to be more rigid you'd just need to add a spacer underneath or something. I've seen people use everything for this. Some head units will come with a rubber stopper you can use/cut to size, or you can go to Bunnings and get that trim-to-length pre-drilled metal mounting strip stuff, or you can even just put a piece of wood or something under it. It depends how heavy your head unit is, I suppose.