Low Power Pin Change Detection (ATtiny)
The additional 80uA drain is almost certainly coming from the pull-up resistor being shunted to ground though the reed switch.

https://www.wolframalpha.com/input/?i=(3+volts)+%2F(50k+ohm)+in+uA

As suggested by @Edgar Bonet, one way to greatly reduce this drain is to disable the pull-up immediately when you wake from the pin going low. At this point it is possible for the pin to stay low even if the switch is no longer grounding the pin, so you need to periodically check it using a watchdog.


Wake from pin going low pin change interrupt
Disable pull-up (stops current flowing though resistor)
Do your logging operation. 
Enable a watchdog wake up 
Go back to sleep.


At this point you can wake either from (1) a watchdog or (2) pin change if the pin goes high again. 

If you wake from a pin change...


re-enable the pull-up
disable the watchdog
go back to sleep


If you wake from the watchdog...


re-enable the pull-up.
if the pin is high now, disable the watchdog and go back to sleep.
if the pin is low, disable the pull-up and leave the watchdog running and go back to sleep.


The watchdog timer on this part should only use single digits of uA while running, and it should only need to be running while the switch is grounding the pin. You can set the watchdog timeout to be quite long- on the order of seconds even, to reduce the frequency you  wake to check with the pull-up (and therefore the net power used, at the cost of latency for detecting pin changes). The main downside to this strategy is that you can miss activations that happen inbetween your watchdog wake-ups, so for example if the pin goes low and then you set the watchdog for 8 seconds, and then the pin changes high and then low again during the next 8 seconds, it is possible (but not assured) that you could miss the second event, so set the watchdog timeout to be short enough that you will not miss consecutive events that you care about (you might not care if the door is opened twice in the same minute anyway). 

Also, as noted by the famous @nick gammon, you might be able to get lower than 5uA when sleeping without the watchdog. Check to make sure you are disabling everything in the power register and that all unused pins are in input mode (these will be disabled when sleeping as long as there is not a pin change interrupt on them).  There are lots of googleable articles on minimizing ATTINY power during sleep.  

You also mentioned that your dominant case is that the switch is closed rather than opened. Since this is the higher-power case with the current switch consider using a normally open switch rather than normally closed one if possible.

Finally, if you just want simplicity and you only care about events of a minimum duration (saym then door much be open for at least 1/2 second to be noticed), then you can skip the pin change interrupt completely and only use an always-running watchdog to wake periodically and very quickly enable the pull-up and check for the desired pin state, and then disable the pull-up and go back to sleep. You should be able to do this in less than a dozen cycles so the net power usage should be almost as low as the watchdog timer drain by itself.