the US 59/ Future I-369 main lane overpass construction (and associated frontage road work) at FM 3129 in Cass County .... I believe it will be the first non-Texarkana, post-I-369 corridor designation, and interstate-grade upgrade, section upon completion.
Google Maps has now updated its imagery (which includes a labelled U.S. 59 Frontage Road), as well:
That's going to be the exit used by residents of the town of Domino/International Paper employees. I wonder will this be the last exit on future I-369 before the road veers off and heads toward I-30?
Recent discussion about I-369 in another thread discussed, among other things, a possible "new" western routing for I-369 in the vicinity of Texarkana, a possible I-49/ I-369 interchange north of Texarkana, and how development north of the current I-369 northern terminus would make a connection to I-49 from that point unlikely at best. The discussion also reminded me of the above question. The short answer is that we don't even know for sure that there will be a new terrain western route of I-369 from some point north of the Sulphur River bridge to I-30 near TexAmericas Center.
The potential for a western routing (commonly known as the "West Loop") was anticipated during environmental studies along the eventual I-49 corridor that included a "Northern Loop" from I-30 in Arkansas to I-30 in Texas (the study basically anticipated using the then currently existing Texarkana Loop south of I-30, with a slight new terrain addition along I-49 in Arkansas). The
Executive Summary of the Texarkana to DeQueen US 71 and Texarkana Northern Loop Final Environmental Impact Statement ("FEIS") anticipated the possibility that US 59 south of I-30 would be relocated to the west, which would necessitate new environmental and location placement studies for the Texarkana Northern Loop (page 14/24 of pdf; page ES-13 of the document):

This map from the FEIS Executive Summary shows both the Texarkana Loop routing of US 59 and the Northern Loop and a potential US 59 relocation and Northern Loop routing, as well as the location of the I-49/ I-369 interchange (same location under each alternative) (p. 15/24 of pdf; Exh. ES-3 of document)
*:

As an aside, it should be noted that AHTD raced ahead of TxDOT and has completed its section of the Northern Loop (greatest DOT upset ever?). To be fair to TxDOT, the Texarkana MPO has studied
a potential corridor for the West Loop and the Northern Loop:

However, neighborhood opposition and lack of funding basically made that effort stall. Since the stall, the I-69 Corridor has gained momentum throughout Texas and the Segment One Citizen Committee identified three priorities along the I-369 corridor: designation of part the Texarkana Loop as I-369, a Marshall relief route, and a Texarkana relief route. In agreeing to the I-369 (then referred to as I-69) signage on the Texarkana Loop, the Texarkana MPO made it explicitly clear that they still wanted the "relief route" to the TexAmericas Center, as reflected in
this post:
the Texarkana MPO adopted Resolution 14-2012 supporting an I-69 designation:
NOW, THEREFORE, BE IT RESOLVED BY THE POLICY BOARD OF THE TEXARKANA MPO, THAT THE BOARD SUPPORTS CO-DESIGNATION OF THE PORTION OF US 59 FROM I-30 TO THE JUNCTION OF LP 151 AS US 59/I-69. THE BOARD ALSO SUPPORTS:
SECTION 1: IMPROVEMENT OF US 59 TO INTERSTATE STANDARDS through the State of Texas consistent with recommendations developed by the I-69 Corridor and Segment Advisory Committees; and
SECTION 2: participation by the Texas Department of Transportation in the EVALUATION OF ACCESS TO/FROM US 59/I-69 and the TexAmericas Center, an Intermodal Freight Facility, along the west side of the Texarkana Study Area Boundary, including the need for DEVELOPMENT OF AN I-69 RELIEF ROUTE as described in Texarkana MPO Resolution #3-2011 ...
Resolution 3-2011 describes the relief route as follows:
WHEREAS, the Texarkana MPO is supportive of the continued study and development of a relief route under the guidance of the Texas Department of Transportation and the direction of the I-69 Segment Corridor Committee One, as described below:
Beginning at the north end of the Sulphur River bridge and concurrent with existing US 59, then connecting to the TexAmerica’s property (former Lone Star Army Ammunition site) and continuing to an interchange point with I-30 ...
Two of the three I-369 priorities have progressed: I-369 has been designated and signed along part of the Texarkana Loop, and a working group has developed a recommended corridor for the Marshall relief route. No similar apparent progress has been made regarding the Texarkana relief route. Since it has been identified as a "priority", progress towards identifying the corridor and achieving a solution with the neighborhoods might be made in the relatively near future.
Identification of the West Loop routing, if any, is a prerequisite for identifying the routing of the Northern Loop. The
I-69 Segment One Committee Report and Recommendations contains an interesting map which shows the Northern Loop as an "I-69 connecting route", as well as showing the West Loop as the eventual primary I-369 corridor (and doing a horrible job of showing both I-49 in Arkansas and the I-49/ I-369 interchange location) ... (page 21/155 of pdf; page 15 of document):

At least the Northern Loop is on the radar, even though it is not a priority.
Above said, a second short answer to the above question is that it is time to hurry up and wait.
edit *Here is the proposed logging of the entire I-49 corridor in Arkansas (and Texas).
http://www.arkansashighways.com/forums/I-49-Proposed-Mileage.pdf
Proposed exit numbering from the Louisiana State Line (through Texas) and to the Polk County, Arkansas line:
http://www.arkansashighways.com/forums/I-49_Exits_1.pdf
Please understand this is all PROPOSED and is subject to a tweak every now and then.
(above quote from Texarkana (Future I-49, I-69 Spur) thread)
Here is a snip from the logging that shows the mileage in Texas;

Here is a snip showing the proposed Texas exits:

above quote from (
I-49 in Arkansas thread)
I assume that Exit 44 in the above snip of the Texas I-49 exit numbers will be the eventual I-369/ I-49 interchange location; it provides a good visual approximation of the I-369/ I-49 interchange location in mileage terms.