Water – use duct tape instead of a draft hood

Looking at the specifications on the page you linked to, it appears to be made of the same basic materials as other duct tapes: plastic coated fabric with a rubber adhesive. Premium Grade it may be, but I think you'll run into the same problems -- it'll get brittle and crack with age. I've used aluminum foil tape where I've needed spot repairs; Home Improvement 1-2-3 says to use duct mastic when installing ducts.

I found this article very useful: Can Duct-Tape Take The Heat?

Duct Tape Cannot Take The Heat

Although our testing has not been able to differentiate amongst other sealant products, the data shows that cloth duct tape is not a good sealant for use in ducts that operate at much above ambient temperature. We believe this is due to the rubber adhesive, but cannot state so definitively. For the most part, cloth backing and rubber adhesives go hand in hand. Thus it is not surprising that the other sealant products have not demonstrated any of the failure modes we have seen in the duct tapes. There are a few products that use rubber adhesives with non-cloth backing and we intend to test these in the future.

To address your side note about Class 1 ducts: from the scope for UL 181 Standard for Factory-Made Air Ducts and Air Connectors

Class 0 - Air ducts and air connectors having surface burning characteristics of zero.

Class 1 - Air ducts and air connectors having a flame-spread index of not over 25 without evidence of continued progressive combustion and a smoke-developed index of not over 50.

It's unclear from your description, but is there an existing vent you're trying to connect to, which is 10x3.5"?

You ran 12x3.5" and are trying to connect to that? The simplest way is to find a reducer to go from 10 to 12". I'm not sure if it's a standard part or not (probably not), but a sheet metal shop (or HVAC) supplier may have it in stock or can make it for you. It's not overly expensive to have them custom make a part like this (in the range of $40 to $100).

If you can replace the existing duct that would probably be better: the bigger the duct, the higher the airflow and lower the noise. It's also easier to find round reducers, so if the wall cap is round (which many are), then you may be able to just use off-the-shelf parts to do everything.