I will increase the spacing to 1.5", and replace my LM334Z's ~68 ohm resistor with a resistor of ~27 ohms.
For the LM334Z this calculation is:
ISet = (227 uV * T) / RSet
Where T = the ambient temperature in degrees Kelvin.
Calculating for 70 degrees Fahrenheit ambient temperature (which is 294.11 degrees Kelvin) and a circuit with a desired 2,500 uA of current (which is 2.5 mA, or 0.0025 A) is as follows:
ISet = 0.0025 A = [(227/1,000,000) * 294.11] / RSet
Simplifying and rearranging you get:
RSet = (0.000227 * 294.11)/0.0025
RSet = 26.7 Ohms
This should hold current at a constant 2,500 uA (or 2.5 mA)