Super Duper Vdd stiffening required on 555 timer, what is the best way?
Your measured short-term stability is about +/-0.01%, which isn't bad for an uncompensated RC timer. 

You can improve it by using low temperature coefficient resistors and capacitors in the timing circuit, maybe by bypassing pin 5 to ground, by isolating the circuit thermally and electrically, in the extreme controlling the temperature in an oven, powering it from a battery with an ultra-low noise linear regulator and capacitance multiplier stage, and using opto-isolation on the outputs. 

But that's just silly. Use a crystal, they're cheap and orders of magnitude better. For example, a 100kHz crystal, oscillator (74HCU04 + a couple resistors + load caps) and a divide-by-four (eg. a 74HC74). Tolerance (absolute accuracy) of that particular linked crystal is +/-30ppm or about 0.75Hz in 25kHz. Short term stability will be much better again.  

There are also programmable oscillator products you can order, there might be one in a useful range for you.