My confusion comes in where my recipe guide says "after all apparent bubbling has stopped for approximately 3 days, and if the specific gravity is where it needs to be (1.062 is what my guide tells me) then the beer is finished fermenting".
Specific gravity is generally measured at two points (for extract brewing). The original gravity (OG) is just before pitching yeast, and FG just before bottling. For a 1.062 OG beer, the FG would almost certainly be 1.010-1.020.
Everyone that I've spoken to in the homebrew world said I need to actually wait two whole weeks after primary fermentation comes to a halt, not three days, then siphon the beer into a secondary fermenter and keep it there for two more weeks before bottling.
That's really just egregiously bad advice. It can definitely be helpful to wait a minimum of a couple days to let the yeast metabolize some off-flavors, but after an otherwise healthy fermentation the yeast can be removed at that point. The only exception would be a true "secondary fermentation" where you want the yeast around to ferment sugars, fruit, etc.
That said, there's also no benefit to a second transfer unless the beer will be aged for months or more, so you might as well just leave the beer in the fermenter until you're ready to bottle. If you're able to drop the beer down into refrigerator temperature range for a couple days before bottling, so much the better clarity-wise.
I didn't see any mention of dry hopping, which would be typical for an American IPA, but if you're going to, now would be the time to do that, assuming the gravity is near the expected FG.