@chadhickman
You cannot change the parcel type from Administrative to regular parcel type.
If you wanted to change them you can create a new parcel type, copy over the schema, append the data and make sure all association to record has been maintained. TEST!. then remove the old parcel type and delete the feature classes that were associated to that parcel type.
Can you add topology rule to the parcel fabric topology - YES you can. You bring a great use case to extend it.
Once you solve the misalignment issue you can consider removing the topology rule.
There could be some creative ways to use geoprocessing tools to automate fixing the misalignment between your administrative parcels and the non-administrative parcel data. We can set up a meeting if you want us to have a look