Some ideas...

Does the living room or bedroom have ceiling can lighting? Often you can remove the cans for access, which will either yeild a cavity all the way to the target wall, or you can use a flexi-bit with extensions through the joists to the target wall.

If there are any appliances on the kitchen partition wall, you removing them might give you the access you need for the other (lving room) side. Cabinets can SOMETIMES be easily removed. No matter what, ALWAYS patch any holes to restore fire ratings to walls... don't just leave the holes open because nobody sees behind there.

On the second floor, you could use the attic crawl space to flexi-bit through the closet wall studs, once you get to the target bedroom partition wall stop (otherwise the bit comes out into the bedroom area). Insert some rods with a light ball chain attached to the end (and wire attached to the other end). Now make your hole on the target wall, insert another flexi-bit to "meet" the rod in the other wall. Remove flexi-bit and insert a "wet noodle" to grab the ball chain. Now pull the rest of the ball chain with wire too.

In the attic crawl spaces on either side, you could also open up the floor in those areas again, yeilding a cavity to the target wall or allowing for the insertion of a flexibit. If you can't easily remove floorboarding, like having to cut through a the solid sheet of plywood, then you're probably better off cutting out some sheetrock from the floor below.

If the second floor has hardwood flooring, often a few boards can be removed and access holes drilled to allow for fishing. Put the hardwood boards removed back right, and you'd never know anyone touched it.

If there are ceiling mouldings, often there is just enough of a gap to allow some creative fishing, giving you "access points" so to speak. Problem is, removing ceiling mouldings is often a destructive process, damaging both the mouldings and wall material.

For the LV wiring only, you could also remove baseboard mouldings and notch the sheetrock or plaster to accept the wiring. That would be least desirable for me, as would running the wires on the inside of closets. Better off making the holes in closet, where patching and painting wouldn't be that noticable.

I think you'll end up getting frustrated and end up making holes for your sanity, but if you truly want to minimize them, those are some ideas I can think of.

Joe