[old_tv_nut]

Bypassing is a good first test.

Wrapping an additional layer of copper tape:
If the outer layer is a ground layer already, this will not help UNLESS the existing layer is bad somehow (or disconnected from ground).
If there is no outer ground layer on the original, adding one will mess things up, as it will lower the impedance (producing transients) and increase the delay. (UNLESS the underlying layer is bad or disconnected, in which case an added outer layer may fix it).

Regarding caps:
Film caps are generally too large in value to cause short video transients, unless they are meant to be bypasses and are open. Transients can be caused if smaller capacitors or peaking coils associated with the delay line are bad.

Regarding replacement delay lines:
Delay lines are designed for a specific impedance, obtained by the number of turns per inch, their diameter, and the capacitance per inch determined by the copper ground sheet or sheets (under and/or over the windings). So the best bet is to get one from the same TV chassis number. Second choice would be to look for one of similar dimensions, although this wouldn't guarantee the winding count.