Of course the Miner doesn't count for collecting gems (for the heart-shaped cut), so you still need to actually find all the different gems, either through collecting in the wild, exploring tombs, or breaking space rocks.
You don't need "all" gems, you need 10, with WA installed you can get it without any of the rarer gems. With the collecting guide maps it should take you a sims day or so to get it given you take a short trip to france and find at least one of the rarer gems, if you got no luck than it might take up to 3 days but that would be surprising.
Actually I think it might be easier and/or quicker to take a few trips to Egypt and collect urns and sarcophagus fragments there to create a bunch of mummies. With my style of playing I would choose the mummy creater route.
I thought about mummies, too, and gave it a try. It depends on how you count the "time", there is also a big luck factor in this LTW (no matter the way you choose). I think that in real-life time, inventing is fastest simply because you will spend almost all your time in fast forward as it requires little micro-management. If you count it in sims days though, it can get pretty close and luck in finding the pieces will pretty much make the difference as inventing is limited because it needs to grow lifefruits (never had trouble finding rare stones with miner), and mummy probably win in terms of non-travel days. And easy... well the inventing path revolves around 4 commands (invent, read book, tend garden and drill) so as far as easy goes... that is pretty much it. But nothing in the sims is particularly difficult anyway.