I understand the task to be performed. Search and rescue of missing people is very similar to recovery of a high altitude balloon payload. Your total search area is somewhat defined, but the final search area is unknown. 

How is the APRS/OSM map detail used to locate the missing person? Are you using the map to be able to locate various resources, LKP (last known position), ICP (Incident Command Post), IPP (Initial Planning Point), for tracking the search teams, for defining search areas, and others?

You are probably not using the maps for physically discovering the missing person.

If you are searching an urban area such as this:

Here it is at zoom 17,

and again at zoom 19.

Zoom level 19 much more in detail, but it will take 16 times more storage space. I would argue that looking at the zoom level 19 maps will not help you find a lost individual any better than zoom level 17.

If we compare a rural wooded area like this:

at zoom level 17,

versus zoom level 19.

We once again don't see any more detail. There's no way to find a lost person under a tree in either map. 

However both zoom levels would be able to show a representation of where search teams may have travelled. You won't know every bush and rock that the search team looked at, but you will have a record of the area that they would have travelled through.

I'm not trying to tell you how you need to run your operations, but rather just trying to ensure that you are not wasting a lot of time and resources downloading a huge amount of data that provides very little added value.

As a further suggestion, have you looked at other APRS clients for SAR use? APRSISCE/32 is not designed for real time tactical operations such as SAR. It does not have a lot of capabilities that would be handy to have for SAR operations.

Xastir was the first APRS client that supported SAR activities, and had some tools built in that were useful for SAR work. Xastir can be a little strange to work with if you aren't familiar with it.

YAAC has some features that make it able to support SAR activities, and it is fairly easy to use.

SARTrack is specialized APRS tracking software that is specialized for Search and Rescue operations. https://www.sartrack.co.nz/ I have not used SARTrack myself, but am very impressed with the functional capabilities included in the software. 

SARTrack is probably the most complicated APRS tracking software out of the four programs we are talking about. I suspect that SARTrack requires a full time dedicated operator sitting at the console to make use of all the functionality. It probably also will require the most effort to learn and understand its operation as it gathers the most detail about a SAR operation. If one is familiar with SAR operations, I would suspect that much of the functionality would be familiar to the operator, and they would just need to learn the buttons to press, and not have to learn the SOPs of SAR.