Ballast resistor will make your circuit's productivity less than 21%, so
terrible waste of energy, even being one of the most safe and cheap
solution.

With a productivity around 70 to 80% you could build a voltage inverter
with discrete components (since it is difficult to find step-down chips
with input voltage higher than 50Vdc).  Perhaps a simple 200Hz
oscillator made with logic gates (74HCT00) and a FET transistor driving
a small power transformer (110 x 24) would generate around 16 Vdc. 

Your control circuit would simply turn on/off the oscillator.

                         +80Vdc        Diode
                              | .------->|---o---------.
                       Diode? 3:C            |         |
                              3:C            |     .-------.
__--                          3:C     100µF ===    | Relay |
           .------------.     | '--.        ---    '-------'
Control----| Oscillator |--FET     |         |         |
           |   200Hz    |     |    |         |         |
           '------------'     |    '---------o---------'
                              |              |         
                             Gnd            Gnd       

I guess this solution can cost you less than $15.  For sure better
designs can be made but this is the idea.

Oscillator:  $1
FET:         $1
Transformer: $7  XFR1635Q (Jameco)
Diodes+Cap : $2

Other idea is just use an adjustable pulse simetry oscillator, and drive
directly the solenoid coil with a FET, you can call it a PWM driver.
             
                        +80Vdc
                          |
                          3  Relay Coil
                          3  & Diode
                          |
            Assym         | 
Control---Oscillator---FET
On/Off      15%ON         |
                          |
                         Gnd 


You should find the best oscillator frequency and simetry to keep the
current curve never going above 700mA.
I guess this would cost you less than $3.

Wagner