A cheap 40 watt iron with a tapered chisel tip will do the job. A conical tip would not get enough contact with the joints to melt them quickly.
Don't try to clean the flux residue on the circuit board. If you do, some of it will get on the inside of the window and mess up the calibration.

 

Success! (Well part way at least we'll see how badly I fried things when I try to reassemble it.)

So, assuming I'm using the meter correctly, it is reading 2.3k-2.4k meaning the bands are not orange but instead faded red. I'm posting photos just in case anyone spots any issues.

Now I'm looking for a 2.1k-1.9k as a replacement. Is there any way to test how these will effect the meter without having to solder and de-solder each one?

 

You could try a skeleton preset resistor say 3.3K and trim it to the correct reading, then measure it and fit the fixed value resistor.

 

An alternative way would be to reconnect the resistor and solder a few inches of insulated wire to each end of RS. You can then reduce its value by connecting a resistor in parallel. Just twist the wires with the new resistor's leads temporarily until you find the right value, then you can solder it in parallel with RS..

 

Well, I've de-soldered the left resistor and put in a couple of leads that I can clamp to new components. The resistors changed the light meter, but not as much as I was expecting. Even with only a 110 in there, I could only claw back 1.5 stops of light.

Switching the batteries from the recommended 1.35v to 1.5v got me another stop and puts me right around where I need to be. I still need to test under more light conditions but right now things are looking good.

Do I have to worry about going too low on the resistor?

If the resistor is that low, does that have rule out any battery types? (currently using SR44 silver oxide for the stable voltage, but I have 40 lithium ones laying around)

 

Spoke too soon, looks like I'm losing linearity on the top end. Looks like more tweaking is in order.

 

In that case, try putting the original value back for RS and try increasing the value of RP. It appears that the photo cell is not as sensitive as it used to be.

 

It appears that the photo cell is not as sensitive as it used to be.

As predicted. I agree it may be hard to replicate the original sensor but the current old one is very far from the original anyway. Replacing both the sensor and the trimming resistors may be the answer.