Re 'your' black data cabinet, there is probably a number on the lock which can be used to order a replacement key for a couple of AUD.
Getting your existing/new internet down to the new bunker. There does not appear to be much space in the ducting between floors run another cable.
I can see a number of possible ways, none of which are 100% kosher:
A) The existing TP phone lines.
B) The soon to be redundant existing cable (CAT5?) from 'your' data cabinet.
C) There maybe an existing unused CAT5 cable.
A) I don't know how readably available DSL type equipment is, but I am sure it appears on eBay etc. However, it is not fast. A couple of cheap hacked Powerline Network Extenders could be used to inject a signal through the CAT3 cable. Hopefully it will not cause much interference with neighbours still running A/VDSL.
B) Once you switch over to NBN you old provider may just abandon the equipment (if no one else uses it). In any event I assume it already has CAT5 between the Lab and Basement Rack. It would be no brainer to 'reuse it'.
Then there is just a matter of running (and hiding) a new cable between the Comms room and storage area.
BTW. I agree with Big Clive regarding your electronic hording :-)
Looks like there are off the shelf solutions to hacking Powerline Extenders:
https://www.startech.com/en-ie/networking-io/110vdslextgbhttps://www.perle.com/products/ethernet-extenders.shtml