The other problem with the NFPA codes is the generic "unlisted" category.
If you have a stove and don't have a "modern" manual for it (think old coal stove) that lists NFPA/UL clearance recommendations, you get to start at "36 inches minimum clearance" and then start with any reduction methods from there.
If you have a stove and it says 18" clearance, you get to start there and apply any reduction techniques (often down to a minimum).
Both stoves could be identical in construction, but one will get your home owners insurance cancelled, because the "inspector" can't use his head for more than a hat rack.
Which is the point about making the code FREELY available. It is treated as fact and law, yet the details are hidden from the public eye.
More to your specific situation: Horizontal runs of pipe might be treated differently than vertical runs. I didn't see any references to horizontal runs in that section of code posted above (nor in the Hearth source pages).
And the rant about generic clearances would likely apply to "building your own" triple wall or whatever pipe. If it doesn't have a mfr UL number and recommendation on it, the laws of physics do not apply- at least according to most insurance companies.
Whatever solution you use, be sure to meet the safety regs- AND keep a copy with your furnace. In my experience, the inspectors don't know the details, just the generic. It's up to YOU to prove it is safe.
As for elbows, are you talking about at the top or bottom of your vertical run?
Many of us have a tee at the bottom with a cleanout cap on the lower end, and a tee at the top with a cap on the one horizontal end as a cleanout for the horizontal run.
Here's an early pic of mine, showing the top tee. The bottom elbow was replaced this year with a tee as well. Had some trouble finding a heavy gauge tee until now.