You’ve been given advise on how it’s supposed to be done, behind baseboard, also that’s how an electrician would do it, unless you specifically told him not to. A junction box would be the incorrect way to do it, also there is no way you have a foot of slack in the existing wire to put a junction box in. Taking the moulding strip off is really simpler than you are making it out to be. If your painter sealed the top edge of the strip, just score it with an xacto knife, pry the strip off with a shark tool, run wires, put strip back on, reseal top edge with caulk color originally used. Make sure to use a wide putty knife behind shark tool on drywall, to protect drywall. My wife could easily do it if I looked over her shoulder.