What do you mean expensive in terms of time? the time to get the gold and lapis?
I was hoping to have to mining guide done today but ended up needing to go out so it won't be until later tonight / tomorrow. The short version though is you don't need to build the tier 1 solar array. Yes it is handy, it produces a decent amount of power and will run continuously but, the builder will mine with whatever power you give it. Each block has an associated RF figure to mine it so provide it with little power and it will mine just very slowly. SImply the more RF/t you can power it with, the faster it will mine (up to a limit). So if you can't power it with the solar array, even a single culinary generator or dynamo would be enough to get going slowly. If you can build some power transfer conduits / ducts then you can power the builder with 2, 3, 4, 5.... generators / dynamos which will make it faster and make getting the gold and lapis for the solar array easier.
Chosen Architect does have a pretty good series on Beyond but he does some odd things too. Storage Drawers are a good idea with the builder but you can place the drawer controller directly on top of the builder then the items will go directly in to the draws. You can attach a lot of draws to one controller, mine was set up in a 5 high 17 wide grid of drawers centre on the drawer controller. Though for common items such as cobblestone, diorite, andesite, gravel, granite etc. I'd put void upgrades in the drawers. This means when they hit the maximum 2,048 items any further items are just destroyed rather than filling up other draws else you end up with tens of thousands of cobblestone very quickly.
I hope that makes some sense but I typed it quickly and will get the proper guide posted tonight or tomorrow.