Could clogged exhaust cause codes 13/33 on my furnace, and how do I check and clear?

My Carrier Performance 96 series furnace (similar to the 59TP6 currently shown on Carrier’s website, but I don’t have the exact model number in front of me) has been showing codes 13 (“Limit Circuit Lockout”) and 33 (“Limit Circuit Fault”) intermittently for the last two years, but several repairmen have come and been unable to find anything wrong.

According to the manual, the codes indicate that the flame roll-out switch has been tripped, but it seems like that can’t be the case since the flame roll-out switches require manual reset and I have never done so. The troubleshooting section of the manual refers to other “limit” switches, but there are no such switches installed on this unit and nowhere else in the manual talks about them.

Yesterday the unit spent most of the day alternating between these two codes, and I decided to spend some time watching it. I sat there in front of it for half an hour (holding a carbon monoxide detector and) watching the flames. The flames look exactly as they should, in both low and high stages, and I see no roll-out.

After seeing nothing for 30 minutes I assumed that maybe one of the roll-out switches is faulty and I should replace them, so I put the cover back on and went to order new limit switches. Minutes later, the unit shut off again with code 13.

The second time I sat down in front of it, it sounded like the exhaust inducer motor was struggling a little, and that leads me to my questions:

This unit uses a concentric vent for intake of combustion air and for exhaust, and the pipes for these are around 30ft long. At the furnace end, they have multiple complex bends because of space constraints, then once they reach the ceiling above the unit they head straight across the room to the outside wall.

1. Is it possible that a clog in either (or both) of the pipes could cause this condition?
2. How can I check for such a blockage? If I find one, how can I clean it out?
3. I have identified a much straighter vertical path for the vent pipes. Is it worth cutting them and redoing them?