Has the concrete stopped developing strength? If there is any chance that it will reach sufficient strength with more time, I would probably wait.
Does the design have some latitude? Many times, especially in thick walls, the design may not be governed by concrete strength.
I do not know how epoxy injection would do anything to improve this situation, or even how you would introduce epoxy into an uncracked mass of concrete without voids.
If the concrete is only 10% of required strength, the demo contractor should be able to determine the extent of that weakness as they demo. Do not rely on the rebar alone to hold up the concrete above. You may want to demo and replace in stages, doing one meter wide portions at a time to maintain stability. (Possibly demo and replace in two or three stages.) You can fairly easily remove a "pocket" of concrete. Verify integrity of the reinforcing, install formwork against the face of the remaining concrete. Provide a port on the form into which repair concrete can be pumped and a port at the top for air to escape. Use non-shrink repair concrete (shrinkage compensating, pea-gravel mix with water-reducing admix.) An all sand mortar material can be used, but this could result in more shrinkage.
Once each repair is done and at sufficient strength, demo the next portion.
Make sure the contractor doesn't add water when s/he can't pump the material (ask me how I know that.) Doing so will simply make the mix weak and even less able to be pumped. A good high range water reducing admix (polycarboyxlate) will keep aggregate in suspension and reduce shrinkage, as well as virtually eliminating the need to vibrate the mix once pumped. You will want to beat/vibrate the formwork to assure consolidation at the new surface. Also, you do not need the repair material to bond to the adjacent concrete that will be demo'ed, but you do not want the dry concrete to take moisture from the fresh concrete, so either saturate the existing concrete or selectively apply a sealer. You will want to either apply want a bonding agent above and below or wet the adjacent surfaces to encourage bond. One good method is to install the formwork and then pump it full of water and allow it to sit for a period before draining. Allow it to dry until the surface does not have standing water ("saturated, surface dry").