An update, if you will.
LADOTD had their second Open House Public Meeting last November 30th, where they updated the public on the current status of the Conceptual Design, CSS, and Supplemental EIS studies now ongoing.
They have now reduced the options for the Connector freeway down to 4 conceptual design alternatives in the core area near downtown; two utilizing a continuous elevated freeway, one with a partially depressed freeway with an open trench, and one with a partially depressed and covered (aka "cut-and-cover") freeway.
I have created a post over at my I-49 Connector blog detailing the four alternatives, but for here I will simply illustrate them:
Original Base Case: 2003 Final EIS/ROD Approved Alternative 
This was the alternative that was originally approved in 2003; it is included in this study only as an control for comparison purposes.
1) Concept 4-1 -- Elevated Freeway with Evangeline Thruway Couplet
In this concept, I-49 would be fully elevated throughout the downtown area, with ramp connections to the Evangeline Thruway allowing for indirect access to all the major cross streets serving downtown. Notice how the Evangeline Thruway is realigned near the Sterling Grove Historical District to move both the freeway and the northbound Thruway frontage road away from St. Genevieve Catholic Church and Sterling Grove. Also, Simcoe Street directly flanking the church is severed and diverted through the Second/Third couplet and a combination of Chestnut Street and Dudley Avenue. Mudd Avenue is allowed full connection with the Thruway frontage road system to/from the west, but is severed from there to the east, with the old northbound Thruway from Simcoe Street to Bellot Drive redesigned as a two-way local street.
2) Concept 4-2 -- Elevated Freeway with Evangeline Thruway as "Urban Boulevard" 
This is essentially Concept 4-1 but with the southbound Evangeline Thruway converted into a 4- to 6- lane "urban boulevard" for development purposes. The existing northbound Thruway would be converted into a two-way local street.
3) Concept 6-1 -- Partially Depressed Open Trench 
Under this concept, the Connector freeway would be depressed 10 feet below surface level from north of Mudd Avenue to Pinhook Road, with major cross streets bridged at least 10 to 15 feet over the freeway. Due to the proximity of the BNSF rail line, Johnston Street would have to be elevated over both the freeway and the railroad, causing it to require elevated structures extending westward as far as Vermillion Street. This would cause penetration of the Freetown-Port Rico neighborhood, which was recently designated an Historical District. Notice also how the southbound frontage road has to be altered to cross over the freeway, and how Taft Street has to be realigned to connect with Thirteenth Street rather than its current connection with Fourteenth Street. The remaining cross streets downtown (Second, Third, Jefferson, and Sixth) do get to retain their at-grade crossings with the railroad, but with very steep gradients between the freeway overpasses and the rail crossings. Also, note that due to the need to cross over the freeway, Mudd Avenue is completely severed across the freeway, unlike the Elevated options.
4) Concept 6-2 -- Partially Depressed Cut-and-Cover
This is similar to Concept 6-1, but with the addition of an embankment completely covering the depressed mainline, allowing cross streets and potential business development over or immediately flanking the freeway. The cover would take in the area from Second Street to Taft Street, and the embankment would take the entire ROW of the existing Evangeline Thruway, requiring the maximum of displacements. There would also be issues involving operation and maintenance costs of the tunnel, as well as concerns about permitted Hazardous Materials loads not being able to use the tunnel.
DOTD also published a matrix listing both preliminary findings of ROW and displacements required and the initial costs for the downtown core area.


As you can plainly see, the Cut-and-Cover option would be prohibitively expensive, costing up to double the costs of the elevated options. The Open Trench option is in between.
The plans for the studies are to construct full hybrid end-to-end conceptual alternatives for presentation to the public and the CSS committees next month (January 2017); followed by more detailed Tier III analysis and major agency feedback; and then 3 finalist concept alternatives selected later in the spring of 2017 to be vetted through the Draft Supplemental EIS document and CSS Design Study. After that, a Public Hearing will be held, and the Lafayette Consolidated Government will select a final alternative for implementation of the CSS design.
Meanwhile, opponents of the Connector are already rearming themselves for a new battle; this letter from Connector opponent Dennis Sullivan posted during the November 30th Public Meeting by opponent Roger Peak over at the Sierra Club's anti-Connector "Y-49" Facebook page encapsulates all the arguments opponents of the freeway are offering.

I'm already preparing a rebuttal to Mr. Sullivan's nonsense, which will be posted to the Connector blog soon.
In the meantime, I've posted some of the Connector Open House Public Meeting documents (accessible via Scirbd) over at the blog. Please feel free to go there and view them; or view the originals at the Lafayette Connector website.
http://redgarterclub.com/RGClubNetwork/buildi49lafayetteconnector/2016/12/10/nov2016update-openhousemeetingdocs-ecifinalcharrettereport/