As noted above, successfully getting the specific configuration you want is not a passive endeavor; you have to be proactive, know what you want or can accept as an alternative, check frequently, and be prepared to pull the trigger (almost literally; Apple's terms state that a sale isn't assured until they've accepted your payment, so it's possible for the rug to be pulled out even during the checkout process).
At some point, Apple revamped the refurb site and actually made it harder to quickly discern which configuration is which from a quick glance at the boxes on the store page, except for the standard configs which show the original price and savings; those can easily be ignored.
If you've come across the item, but have missed out on it, save the link and use it to quickly jump directly to the desired config. If the magical "Add to Bag" isn't greyed out, pounce.
When I was looking, I found that Apple tends to release stock mostly in batches, with the selection suddenly going from barren to flooded. As it sells it, keep trying, as stock is sometimes replenished. If at that point, you dawdle, or start to debate again, you may miss out, so that goes back to knowing what you want and being ready to buy.
It also helps to check during what are considered off hours, when most people are in bed, and not shopping.
Mostly, it boils down to knowing the target, and the right timing.
Also keep in mind that the clock starts ticking on AppleCare+ from the date that
it is purchased (
*1,
*2), not on the date of the original machine purchase, and that you have 60 days to decide. So however long you wait to buy AC+ effectively results in a small bonus period depending on how long you wait, up to those 60 days.
*1) ("…coverage to three years from your AppleCare+ purchase date…")
*2) ("Coverage begins when you purchase the Plan and continues through, unless cancelled, the date specified in your Plan Confirmation (the "Plan Term”).")