Analogue current and voltage regulation and rectification thereafter
Since you have a variable voltage setup already then you can reduce the current by reducing the voltage, obviously, and then crank up the voltage later. If you want this to be controlled by a circuit automatically, then yes you can add a timing circuit that slowly ramps up the voltage.
Now if your asking if there is a way to limit the current but keep the voltage the same.. the answer is, no, not really (though it may seem that way). Remember the liquid in your solution is a resistor. It changes with temperature but at any given temperature its resistance is a fixed value. Because of the fundamental equation \$I=\frac{V}{R}\$ well if you aren't willing to lower the voltage, and since you cant change the resistance of the fluid (short of changing its temperature) you wouldnt be able to effect the current. Of course you also mentioned adding a lamp or resistor in series, but in reality that is the same as lowering the voltage except it would be a more wasteful way of lowering the voltage. Imagine your liquid is 100 ohms and you apply 100 Volts to it, you would have 1 amp flowing through the liquid. Now if you add a 100 ohm resistor in series with your 100 ohm fluid you have now reduced the current to 1/2.. but if you measure the voltage across the fluid it will be 50 volts, and the voltage across your resistor will be 50 volts. So from the perspective of the fluid it would be completely identical to having just lowered the voltage to 50 volts, which would produce the same current, except by putting a resistor in series you are wasting twice the power.
So you have two options:

Adjust the voltage to create the current you want, either manually, or you can design the circuit to do it for you. This would be called a current source if you want the circuit to automatically keep a fixed current.

Apply cooling to the fluid


If you want is a circuit where you set the current, and it adjust the voltage dynamically to keep the current constant, and is capable of 170V (basically a variable current source rather than a variable voltage source).. then yea you would need to design a circuit that first senses the current, and then a controller to something like a variac that is fed into a rectifier.