I've always considered the load factors and even beta factors to increase as our understanding or lack of understanding for what future loads could be applied to a structure.

So, for example, if we're backfilling a box culvert and there is some fill, the only likely source of additional loading will come from the surface and will be transfered through arching action in the soil.  Thus the impact can be relatively small.  In many cases, the DOT will own the right-of-way around the structure and significant loads will not be placed in the vicinity.

A frame, above ground, will not provide the same level of comfort.  Many things may happen around the bent to change the nature of the loading.  As is common here in the midwest, we see fill slopes that used to taper off through the frame and now the roadway is being widened and a retaining wall is being placed in front of the bent frame and so the soil height acting on the frame has increased.

As for the temperature out of the ground...a box culvert is usually significantly reinforced and does have the minimum provided by AASHTO in 99% of the cases ( I have to believe).  I don't know why, other than laziness or ignorance, that you wouldn't look that if you feel the structure is subjected to large temperature differentials.

For AASHTO 15th edition RCB's are considered as culverts in design.  The beta factor of 1.3 is for lateral loads on retaining walls and rigid frames EXCLUDING RIGID CULVERTS.  The beta factor of 1.0 is for vertical soil loadins.  For buried structures, temperature has not been much of a consideration as the soil is considered to stabilize the temperature range.
If I understand properly you are going to constuct a center wall to match the two exterior walls, and then construct two 28' spans (with minimum fill) on the walls.  Is this correct?
The exterior walls (if backfilled) were probably designed as a retaining wall (cantilever) with the majority of reinforcement at the outside face and T&S on the inside face.  Or? was the wall designed for this future expansion?  

If the walls were designed as retaining walls and you place the slab on it, this connection will be a simple bearing connection, unless you attempt to make a moment connection by drilling and grounting rebar into the wall.

I would treat the existing wall as an "abutment" for the proposed spans with a simple/pinned connection for the slab to abutment.  If the wall has the capacity for this loading, continue.  I would note that if the wall is excavated, the loading characteristics of the wall could change resulting in a significant tensile stress in the inside face of the wall. Check out all the possible load conditions for the wall.

I have done this on much smaller spans with no problems but have not the experience with a span of your size (28').  Hope everything checks out, best, Tincan.

I have done this in much shorter spans where the moments were not of the magitude of your situation.

I live in a cold climate.  Frost can be up to 12 feet deep under a highway that experiences the application of salt.  The fill around a concrete box is also frozen about 2 to 3 feet around it if the wind blows through it periodically (except the floor).  The warmest it gets is about 65 F inside and about -40 F in the winter.  This equates to a change in temp of 105 or approaching a change in length of 1" every 100'.  Unknown is the effects of frost expanding around the concrete barrel while the barrel contracts.  I have noticed almost all have circumferential cracking that can be as wide as 1/4" or control joints as wide as 4".  I have never seen a concrete barrel have structural problems including those that have indications of poor construction and poor rebar placement.  Almost all have a slight bow of the roof with a longitudinal hairline crack along the inside of the roof.  The main problem I have noticed with concrete boxes is that they outlive the creek characteristics and are left with an outfall due to stream degradation downstream.  Regarding the temperature problem, you might want to consider putting in control joints every 50' and make sure you collar all four sides and would suggest non-woven geotextile layered to provide enough structural strength for a 150 mm gap because the boxes will move apart that much in 100 years in clay fills (we use strutural granular fill around the barrel now and this may solve drifting).  Concrete boxes are being replaced by corrugated steel-soil structures due to economics and I think it is sad because they provide so many more benefits than culverts.  I am a staunch advocate of concrete boxes and suggest putting the date in the concrete (and your initials if boyish).

Pug makes a good point that others haven't addressed in the replies above.  Most DOT require expansion joints every 50' with 75 being the max.  

Those expansion lengths are not just for temperature either.  In many cases the maximum length of a 5/8" rebar is about 60'; any longer and there are transporting and lifting problems.