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Fun stuff, and congratulations on the new family member.
A couple of things to consider:
Carrier Current (through the park’s wiring accessed via your unit) might give some results. In addidtion to what PhilB noted about the Carrier Current effect of the power supply, you could try wiring the antenna output that way too.
The Low Power Radio Communications (L.P.R.C.) Tech Page has several items on Carrier Current as well, including Carrier Current Part 1 and Carrier Current Part 2 and Carrier Current Techniques
You would still use a loading coil, but you would be loading the portion of the wiring that ran between you and the next step down transformer from the utility company. That would give you the physical presence of an outdoor antenna without installing one. If there are no transformers between you and the other units (not too likely, unfortunately) then you would have a park wide Carrier Current system.
Two obvious cautions – watch out for the hazards of working around mains power and remember that everyone else is in a Faraday Cage too, and will have a difficult time tuning AM in their boxes.
One way to mitigate the latter might be to make and give away instructions for the Easy to build AM receiving antenna for your radio
Experimental broadcasting for a better tomorrow!