One method used is to snake a garden hose up to the roof to where the vent line protrudes from the roof. An expanding bladder of the size to fit inside of the vent pipe...
.. is attached to the hose and then pushed down into top of the vent pipe. A helper on the ground then turns on the water to the garden hose. The bladder expands to seal against the inside of the vent pipe and force the water to go down into the vent toward the plug up.
Success of this scheme will depend to large degree if the blockage in the vent is a total closure of the pipe or not. A partial blockage may just let the water run by and not provide much help.
The ultimate standard is going to be your local building department and inspector, but the International Plumbing Code only specifically prohibits plumbing in elevator shafts or in elevator equipment rooms (301.6). The only requirements specific to location of venting deal with size, distance, and type of connection to the system that they are venting. Everything else is deferred to the International Mechanical Code.
For chimneys that are used only for venting gas-fired appliances, the IMC defers to the International Fuel Gas Code. The relevant portion (501.15.4) of that code states only that there be airspace clearance to combustibles per the International Building Code. Note that there is a specific exemption for masonry chimneys with a low clearance liner.
This gets you back to what it appears that you already know from your question (R1003.18) "Any portion of a masonry chimney located in the interior of the building or within the exterior wall of the building shall have a minimum air space clearance to combustibles of 2 inches (51 mm)." However, again this is exempted if a low clearance flue liner is in place:
Masonry chimneys equipped with a chimney lining system listed and
labeled for use in chimneys in contact with combustibles in accordance
with UL 1777 and installed in accordance with the manufacturer’s
installation instructions are permitted to have combustible material
in contact with their exterior surfaces.
PVC will ignite at 435°-557°, roughly the same temperature range wood will (although it will be a molten puddle at that point). So, unless your chimney liner is rated for contact with combustibles you would need galvanized or some other form of non-combustible pipe. If you don't know how the chimney is rated, I would take the presence of the existing air gap to indicate that it is not contact rated.
That said, if you can maintain the 2" minimum to a PVC pipe and the local code authority will sign off on it, I'd do it. Oversimplified, a 90% efficient gas furnace would basically dump only 10% of it's BTU output into the flue gas. I don't ever recall finding a brick chimney that was even warm to the touch on the outside, except right next to the inlet from the furnace.
Best Answer
I believe that code requires it to be located at least 1-1/2 inches from the wall (or framing?) face or to be covered by at least 1/16" steel plates (similar to wiring, and for the same reason.) This is why (as implied in @John Gaughan's comment) wet walls are typically framed with 2x6 or even 2x8 rather than 2x4 lumber (that would be a "practice" in the spirit of your question.) Another method is to use 2 separated rows of 2x3 or 2x4 framing, which saves on a lot of hole drilling and lumber cost. Does not prevent the determined idiot from finding a pipe and drilling something longer than code expects into it, but nothing does, really.
On the whole, I prefer PVC - having dealt with corroded metal pipes (those can be drilled through as well.) Providing an actual pipe chase (boxed in, rather than trying to "bury it all in the wall") provides more protection (you can give them more space) and should help keep anyone with the slightest clue from drilling there by accident (because it's obviously a pipe chase.) Plus, you don't need to make the rest of the wall excessively thick.