Plates are the cheapest BP per metal in the entire game (15 metal for 1 bp). The only problem is that they cannot assist, so for that reason I would put them to the side for now.
The second cheapest source of build power is caretakers (18 metal for 1 bp).
After that it's conch (20 metal for 1 bp).
All these are a one time cost to increase BP.
Reading this post, I am not convinced some understand how engery is spent. Anything that reclaims/builds spends 1 E for 1 M. You can see this if you select a con doing something and their stats at the bottom left under the unit icon will show +/- next to the E and M symbols. When you relcaim you spend E, which if you are excessing is taken from the overdrive to convert the wrecks/debris into metal. In short, you reduce your overdrive to spend energy so you can get metal faster. Still, unless you are excessing metal you should always reclaim because overdrive ratio spends more E per M, so reclaim is better income than overdrive.
The point is increasting your build power already costs you some overdrive. Spending more E in a ratio less than 1 to 1 to further increase build power would enter a cascading effect that reduces overdrive and then reduces metal income. Why would I ever enable grid on my factory if a caretaker accomplishes the same goal, but doesn't lower my metal income? No sane person would do this. It wouldn't take very long, no matter the ratio, for the loss of metal income to surpass the fixed cost of the caretaker.
You're suggesting two choices: caretaker wich cost one E to spend one M, or factory grid which costs 2 E (or whatever number greater than 1) to spend one M.
You'd be shooting yourself in the foot.