First problem you have is that he used flex duct, that is not for ventilation, that is for air conditioning or heating. Cooking produces grease and flex duct will trap the grease in the creases and cause you problems and maybe a grease fire. Cooking ventilation requires solid round or rectangular duct.
That being said there are a million different power pack inserts for wood hoods and they probably range in price from $250.00 to $1000.00 depending upon what you want to do. Most of the better units would be 500 cfm or better and they will all work with your circumstances They have units with mesh filters and with baffle filters and vent-a-hood uses a magic lung if you like spitoons. Baffle performs the best over all because it scrubs the grease out of the air and cleans up in the dishwasher. they range in widths from 20" to 58", you could use 20, 22, 27, 28 in your hood and they do install easily. They should be recessed into the hood at least 3" stndard is 4" and that will create the proper capture area that you will need. Some units are also remote control and some will allow for seperate wall switch control is you so desire. If you stay away from the cheap mesh filter units that are probal between 300 and 450 cfm you should be ok. Your biggest problem is the flexable duct that was installed.

Ditto. "... solid round or rectangular duct. "
-- Go to a big hardware store and ask to see "galvanized" duct. It's steel, zinc-coated to be anti-rust.

Ditto. "... power pack inserts ... and they will all work ... with mesh filters and with baffle filters...."
-- I have a Fantech FG6 which is INLINE, i.e. inserted into the duct somewhere along its length, not down in front of your ears!

Ditto, "... recessed ... create the proper capture area that you will need...."
-- Think of it as a sink, turned upside down. The bigger the sink, the better it is at doing its main job of capturing smelly greasey smokey air before it gets sucked outdoors.

----

"... low-fat diets, I almost never fry..." "8" - 10" diameter "
Good! You have a clear idea what you don't need a vent for. You don't need to go to the highest CFM exhausts, which cause problems since they need Make-Up Air to replace the air being blown out of the house. You also don't need to insist on a baffle filter: mesh work too.

----

"... an inside wall about 6 ft from the nearest exterior wall. ... ran parallel to the exterior wall thru which my range hood should have vented. ..."

What is your ceiling height? What about a header box under the ceiling? That is where you run a (e.g.) 4" by 14" duct. Total less than 6" header. If not that, what about soldering steel support on the I beam, at the place where you will Cut The I Beam, to let the duct through to the exterior wall. I would do that. then the duct goes through the I beam. Consult someone else first.

"... build a wood cover to go over my range hood but that I first need to give him the specs..."
see thread below as one example.

Here is a link that might be useful: exhaust hood, custom covered in: Finished White Kitchen

Wow. flex duct for ventilation is a BIG no no. I like Dividro's idea about supporting your I-Beam so you can cut through it.
Broan has an RMPE7004 Power Pack. Liner to match would be RML7030S and then you select an external or in-line blower. 600CFM would be best.

For easy installation Broan also has a hood, E6430SS that a loval cabinet maker loves to use as a built in unit.

Another model would be the Best CP35I309SB. This is a built in but includes the pack, liner, and blower.

These are all under $1000 and would woork fine.

Replace the duct though!!