In a way any coil is a coil even a Tesla Coil:
http://eece.ksu.edu/~gjohnson/tcchap6.pdf
Why not use a "clamping diode" in place of resisitor to protect TCU
"Turn On TimeThe time constant for a circuit with inductance and resistance is T = L / R, so for this clock that's .39 H / 10 Ohms = 0.039 seconds or about 40 ms. It takes about 3 to 5 time constants for the value to settle so let's say it's in the 0.1 to 0.2 seconds area. "........................"When the current is stopped the coil generates a voltage spike that's opposite in polarity from the polarity when the coil was powered. A common way to protect a transistor that's driving a relay is to place a diode across the coil with the diode back biased during normal drive so that when the voltage spike happens it will be shorted out in the diode. This same method will keep the points in a mechanical clock from arcing.
This will slow down the time it takes to discharge the coil. The time constant is the same as calculated above or about 0.1 to 0.2 seconds. So even when these are added toghther they are still much less than a minute.".............................."As current goes into an electro-magnet it charges the magnetic field. If the current is stopped the magnetic field collapses generating a current in the opposite polarity but starting out at the same value. If there is no snubber circuit across the coil the voltage can be very high. This causes arcing on the mechanical points controlling the current input, wearing out the points.
By placing a resistor in parallel with the coil about five to ten times the coil resistance the voltage across the coil at the start of the back EMF will be five to ten times the normal coil voltage and so eliminates the point arcing problem"
Obviously they chose a resisitor to delay the solenoid change time not just to protect TCU, as many circuits in Q use multiple diodes to blow main fuses when battery is jumped BACKWARDS and diodes to protect electronics from reversals!
So maybe some of both a reverse clamping diode [100 volts and a few watts] and a higher resistance resistor x2, or x 3 pr 4x OEM to reduce the spreading of electronic vs mechanical time.
One would use a digital oscilloscope to few and time what happens.
Secure 2-3 from junkyards and try them in series for 2x and 3x.