Best way to add low voltage outlet to wall that has blown in insulation on the other side?
A wireless AP that is power via PoE.  Connect a power injector on the source end of the RJ45 or get a PoE supporting router.

Then you only need a hole large enough to poke a network cable through.

PoE+. PoE+, or 802.3at, provides up to 30W of power to powered devices. 

The upcoming IEEE 802.3bt aka 4PPoE (4 Pair Power over Ethernet) standard will introduce two new levels of power: 55 W (Level 3) and 90-100 W (Level 4).” 

Depending on your access point this may or may not be viable option.

You maybe able to use this 48v to 12v @ 2A to power your AP.

https://www.amazon.com/ANVISION-Splitter-Ethernet-Security-AV-PS12-G/dp/B07W87KSFQ/ref=sr_1_5?keywords=gigabit+poe+to+12v+adapter&amp;qid=1575563331&amp;sr=8-5


https://www.amazon.com/ANVISION-Splitter-Multi-Size-1000Mbps-Compliant/dp/B01JCKHIGM/ref=sr_1_13?crid=2ANY0RN4U0G7M&amp;keywords=12v+poe+splitter+gigabit&amp;qid=1575563721&amp;sprefix=gigabit+poe+to+12v%2Caps%2C148&amp;sr=8-13