So with telescoping casings, the sticking point is that casings will need to be removed as the concrete is placed in stages. The overlap between the telescoping casings needs to be long enough that they can remove the inner (bottommost) casing and still have the next casing contain the slumping concrete from inside the one being pulled as it is removed. Note that the cage needs to stay in place as the casing(s) get pulled. As there is usually a lot of friction on the casings, a crane with a vibro hammer or maybe an oscillator may be required to pull long, heavy temporary casing sections.
The job I worked on where the piling contractor used telescoping casings (parking garage in Chicago) the shafts were designed to have a permanent casing (corrugated metal pipe) matching the nominal pile shaft diameter installed from the stable soil near the bottom of the casing stack to the top. The cage got hung from the top temporary casing, concrete was poured into the permanent casing and sand fill was placed around the outside of the bottom of permanent casing to ensure that the concrete doesn't leak out there. Once the pile was poured to top and let set up (at least 16 hours), additional backfill (sand) was placed around the permanent casing as the temporary sections were removed one by one. These piles were designed for end-bearing only, IIRC.
In your situation, I would require the contractor to describe their proposed methodology in some detail and show that the resulting pile meets the design intent. Get an experienced inspector to monitor their work.
From your description of the pile uplift requirements, I'd have expected a slurry method to be used to construct the shafts - which avoids the installation and removal of casings (and related changes in constructed pile diameter), simplifies cage support during concreting and ensures that you get skin friction from the resulting pile. If the dimensions are feasible (diameter of up to ~36"), I'd also consider augercast technique to construct straight shafts in soils that would otherwise require some sort of excavation support.