Sorry, but that article/process is nonsense. We don't need to use methods from hundreds of years ago.
The only thing that pouring it between different vessels does is introduce more oxygen. Simply aerating your vinegar daily by stirring will accomplish the same thing. You can use a whisk and a little "elbow grease", or a drill stirrer. If you like the rustic aspect, you can make a whisk out of sticks.
For the ultimate fastest production you'd need constant aeration, with either an air pump or continuous stirring. It can be done in 12-48 hours this way if your culture is healthy and you keep it warm.
Pumps do not cost "hundreds of dollars". That's total BS. You can use any cheap aquarium pump, under $10 USD.
https://www.amazon.com/dp/B004PB8SMM/ heck this one comes with an air stone:
https://www.amazon.com/gp/aw/d/B073DWVX5P/ I know you live "in the middle of nowhere" but maybe there's a pet or aquarium store somewhere nearby?
Stir plates for small batches can be built for cheap as well.
Aeration does come with a trade-off. Some of the aromatics will be stripped in the process. Stirring is likely better at preserving the aromatics vs using an air pump.