[old_tv_nut]

You didn't say which terminals of the contrast you are connected to, but if you don't disconnect one end, you will read a bunch of other things in parallel, particularly the delay line and its 1.2K input resistor. So, the 1K reading is probably normal or close to it for an in-circuit reading. I would just wait to see what the replacement coil does for your ghosting, rather than disconnecting things unnecessarily.