I am skeptical about both your techs. I don't understand how a larger vent pipe can create soot and block the heat exchanger, and that if the pipe were 3 feet longer there would have been no problem. If you have a build up of soot, then you may have a chimney draft problem. I could be wrong, but I doubt the draft problem is being caused by the 3 inch diameter. My 40 gallon hot water heater has a 4 inch vent pipe! If the heat exchanger is not cracked, then why is tech number two recommending a new furnance? Why can't vent pipe be fixed if that is the actual problem? You should have the original contractor come in and review the installation. If as you say the installation did not follow Carrier's guidelines, then you have a good arguement about getting him to fund the repairs or replacement.

After reading this entire posts and seeing no definitive answers, I'd figured I would chime in. As an architect I see a lot of projects where we replace an existing boiler with a Direct Vent (DV) boiler. 90% of the replacements use a horizontal, thru-wall vent. This is done typically because it is easier and less costly than going through a roof. Note on the attached link that there are maximum distances for vents and you are limited to where the outlets are in relation to windows, doors, A/C condensers, air intakes, overhangs, etc. You say you could use the 'unused, walled-in chimney' as a vertical vent. I assume this means a wood framed chimney enclosure. You could run PVC vent pipes vertically through this chimney but you would have a difficult time accessing the pipe joints and brackets during installation. DO NOT THINK ABOUT connecting to an old masonry chimney, even if it is terracotta lined. The direct vent gases are cool and will condense inside the chimney fast leaving a pool of highly corrosive water at the bottom of the chimney. This will eventually degrade the chimney and create possible CO leaks. For new construction I typically specify running the pipes vertically with a roof termination. This eliminates the steam plume shooting through the house wall while the boiler is on. Note that Weil McLain requires the pipes to slope back toward the boiler. I believe they collect the condensate and reheat it. Not certain how this works. I know that in a vertical installation there will be less vapor exhausted and more condensate generated as it rises through the pipe. This is typically collected at the bottom of the vertical stack into a condensate pump. This water is corrosive so be careful where it is pumped to (i.e. keep it away from landscaping). As long as you can find an inconspicuous location to vent the gases, the sidewall is the way to go for a retrofit. Here is a link that might be useful: Venting

If the deterioration of the brick is really due to excessive moisture in the chimney flue, adding a coating to the exterior will do nothing to solve the problem. It may, in fact, make it worse. The only cure would be lining the chimney. Here you have two choices: a stainless steel liner or a poured in place liner. The latter will actually strengthen an old unlined chimney because the material bonds to the chimney interior and becomes an integral part of it. There are at least three companies. Supaflu (www.supaflu.com) is the only one I've had direct, positive experience with. If you're having difficulty with rain or assorted creatures entering the chimney, a cap may be worthwhile. If you haven't had any of these problems, I'd say it's unnecessary. If the flashing around the chimney needs replacement, by all means have it done, but I'd certainly pass on any interior coating unless a liner is installed first.

Well, forget the slum lord bit. We have the same set up in our 1st floor kitchen (see photo) and the 2nd floor above it had a blocked opening. I seriously doubt anything nefarious. In our 1st floor kitchen the chimney was obviously used for the cooking stove. 2nd floor -who knows? But certain that it was for heating, and also certain that not every room received a fireplace ($$), -some just got a wood stove. Stranger is that you have (had) lath covering the chimney, which would be a fire hazard if a device was ducted there. But if one was once and later removed, one would think that this would have occurred after the period when wooden lath was used (given your house @ 1919).