Yes. I fit steel junction boxes in places the old wires can reach. Then run EMT conduit between the panel and those boxes. No more than 3 circuits (MWBC counts as 1) in each conduit and use 3/4" conduit, for easy pulling and future expansion. NEC limits each conduit run to 9 conductors (4 circuits: grounds and MWBC neutrals do not count) unless you upsize conductors. I'd use the biggest boxes I can get, no smaller than deep 4" 2-gang boxes, because they will be full of splices. I use THHN/THWN through the conduit to the panel. Terminate grounds at the ground lug in the junction box, or run a wire. EMT is a ground path.

But try this. Leave the panel where it is, and install a sub-panel in public or tenant space. In fact, forward-think: if in the future you wanted to set up the tenant with a separate meter, what could you do now (cheaply) that would make that cheaper and easier later? Setting them up with a sub-panel easily converted into a new main panel, would be awesome all around. This isn't necessarily a large investment, mostly just forethought to not paint yourself into a corner.

Honestly I'm surprised your GC is trying to feather-bed the project with unneeded work when the sub-panel is a really worthy effort.

If you can't get the cable down the wall cavity, then use a junction box to transition to THHN in conduit and go down the wall that way from there

Normally, this run would be inside the wall cavity and then enter the panel from the back -- even if it's somewhat harder to run that way, it has the advantage that you don't have to mess with conduit. If that's not possible, though, the alternative would be to run the NM into a box in the attic, where you transition to THHN in conduit (1/2" EMT or PVC suffices for this) and then run a short length of conduit out the wall into a LB conduit body, then conduit down the wall to a point alongside the panel, where it uses a LL or LR (depends which side of the panel you're on; if you can't be sure when you're buying it, simply pick up an Arlington AnyBODY or equivalent configurable conduit body instead of the LL or LR) body to transition into a nipple into the side of the box -- do not enter the panel from the top! (NEMA 3R boxes require a hub fitting to enter from the top, and generally only have knockouts for a single hub atop the box.)