Countdown to specific date and time (6 months away) and then count up
The obvious solution is a microcontroller, combined with an 9-digit LCD ("_DDD.HH.MM.SS"), but the 9-digit displays I found are a bit large, so let's see what we can do with this one. It's 52 mm x 22 mm x 2.7 mm, so dimensions are ideal. You can place the microcontroller and other components under the LCD.



This LCD is actually a character LCD, not a 7-segment, but you can ignore the segments you don't need. You're one digit short to display the number of days in three digits, but you could use the CA1 segment top left to indicate > 99 days.  

For the microcontroller I suggest a TI MSP430, which has an LCD driver on-chip, and consumes just a few &micro;A when running at 32.768 kHz. Note that a standard crystal has a 20 ppm frequency tolerance and therefore may have a 5 minutes error over 180 days. More accurate crystals exist, you'll pay a bit more for a 10 ppm and a lot more for a 5 ppm crystal, but I couldn't find the latter in a 32.768 kHz tuning fork crystal. This one is available in 20 ppm and 10 ppm precision. The 10 ppm version reduces your error to 2.5 minutes over 6 months. Keep in mind that this is initial frequency accuracy, and that temperature variations and aging (3 ppm/year) also add to that.  

For battery operation you'll have to use a button cell like a CR2430 to fit in the given height. This holder is as low profile as you can get. This battery has a 290 mAh capacity (down to 2 V, no problem for the MSp430), so we'll have to keep current below 35 &micro;A to run it for a year. For the MSP430 this is not a problem (I've done a project where it consumed 4 &micro;A).
The battery + holder is a bit wider than the display, so you'll have to prevent display pins from protruding on the bottom side of the PCB. This is usually costly, but at 1k+ pieces you may have a tool made to cut of the pins, so that they can be soldered on the component side, like SMD.

edit
I thought of adding a DCF77 atomic clock receiver to solve the timing accuracy issue, but dismissed it because of the thick ferrite antenna; even with a 1 mm PCB we'll only have about 6 mm under the PCB. But there's a solution, albeit that the whole will become somewhat longer.  



This SMD antenna is maximum 6.3 mm thick, so might just fit. The receiver module is not a problem, space-wise.  



An advantage of a precision reference is that the MSP430 doesn't have to run off a 32 kHz crystal. If we clock it from a 1 kHz RC relaxation oscillator it will probably consume less than 0.5 &micro;A. Sleep mode and a wake-up interrupt from the DCF77 receiver is not an option; the receiver should be off as much as possible, because it consumes too much power.