Hi R704,
I read your post and then had the strange urge to run and hide somewhere...

My S3 109 GS is my daily driver too, it's the only vehicle I have and has been my daily for a number of years now.
I'm more than happy with the result of all the mods I did, so all I can say is, think it all through and get as many advices/test drives as you can under your belt before you make your decision on what to ultimately do to your own vehicle.
I'm running the Holden 202 and not the standard Rover engine, so I can't advise on what mods the Rover engine would need, other than to say that even with bolt on/ancillary mods, the job won't be small, for once you go down that rabbit hole and add diff gears, perhaps a transfer case and then even start looking at overdriven gearboxes, the common sense element should kick in and give you your answer as to the practicality of setting out on that path.

(I must lack that common sense element

)
I can't advise you on any of that, but should you really want to go that way, then sing out and I will try to call past when out your way, or alternatively you could call past my place or we could meet up half way, in order for you to check out how mine goes.
Mine's probably akin to a hamburger with the lot, so you'd perhaps view it as at the extreme end of the rabbit hole

, being the mild/sensibly souped up Holden 202 engine, high speed Ashcroft transfer, 5 speed Nissan gearbox and high speed diffs with Detroit Locker in the rear.
All I know is, one element alone, be it engine, transfer box, overdrive gearbox, or diff gears, won't deliver all the goodies, rabbit holes sadly don't work that way...
My "quest" began with a stock standard 202, still running points ignition, coupled to the Ashcroft high speed transfer, 4 speed Land Rover box, and high speed diffs. That combination was "ok" ish on it's own, but I wouldn't rave about it, it was just ok. It did the highway speeds and pulled well enough.
A gearbox failure prompted a rethink on what the next step was going to be, and I got lucky and scooped up a Nissan 5 speed box for a good price and set to work. That said, it was by no means a quick swisheroo, it ended up becoming almost a total rebuild of the vehicle, for i couldn't just do one thing and leave something else alone, it went kind of crazy and ended up taking a few months, and lots and lots of research hours were undertaken to see what could/would work and what wouldn't.
Maybe I just got lucky, but the overall result of my build has never left me wanting for it to go any better, and the thoughts I always had of throwing a side mounted blower on it are all but distant memories now...it goes well enough for what it is...I'm content with it as is now, so much so that I rarely touch it or even give it any thought anymore. It's just my transport from A to B, and at the end of the day, it's an ex army chariot...not a modern luxurious ride, though I will confess that I do regularly yearn for a stock standard Commodore of Falcon or something to just cruise in, with auto, power steer, aircon....something that my dancing Elvis dashboard doll would work properly on (not enough dash to dance on in a Series 3

).....ahhhhhh. Ho hum...
That's a rabbit hole and a half you're looking down mate...
Bonne chance!