Tax parcel shapefiles are available from NJGIN open data
NJ Geographic Information Network (NJGIN) Open Data, managed by the NJ Office of GIS
njogis-newjersey.opendata.arcgis.com
Of course, you would need to know how to turn these into a Garmin-compatible map. But it's certainly possible to make a Garmin .img file with a transparent background that you could use with Birdseye. One program that can do this is Mapwel. I used it a long time ago but have no idea how well it works today. Looks like they have a free trial though, so you could play around
www.mapwel.net
I no longer make maps for Garmin devices and am not going to resume. Their map formats are just too limited and I don't want to support their expensive, closed products, sorry. I am doing my part by offering a growing collection of free maps in my own app. For what you want, I wonder if the best bet would be Garmin's own "Huntview" map?
"Featuring exclusive BirdsEye Satellite Imagery and 1:24K scale TOPO mapping"
"Identifies landowner names and boundaries for public/private land types and boundaries, using data from multiple sources for superior coverage and detail"
https://www.garmin.com/en-US/p/646691/pn/010-D1659-01
Looking at the screenshots, I really can't tell what these look like however. Maybe somebody else here has experience with them? There are other companies that (evidently) make maps that show property ownership. Here's a free one, but over 10 years old, no idea how useful it would be
https://www.gpsfiledepot.com/maps/view/180/
If you're using your iPhone, is there no cell coverage for you to use my regular app?