I wouldn't fancy setting up DIP switches on 100+ boards without ever making a mistake, and certainly wouldn't want to solder that many links by hand.
All you need is a way to uniquely identify one board at a time, so it can then become the only unit which responds to a "set ID" message from the master. The master can increment a counter to set IDs sequentially without repetition, or it can assign a single, nominated ID (so you can replace individual units and have the new one keep the same ID as the old one).
Perhaps in this case you could have a single pushbutton, with some logic along the lines of "if the button is pushed within 10 seconds of power-up, request a new ID from the master".
Then all you need is for each slave board to store its ID, and every non-trivial microcontroller has EEPROM or Flash that can be used for this purpose.
My favourite design in this respect was a magnetic sensor, which used multiple, 'smart' sensor boards on a common bus. The criterion for assigning an ID to each board was "if you can see a magnet, and don't already have an ID, then request one from the master". Assigning IDs was a simple as putting the system into configuration mode, then swiping a magnet along the length of the bus. Total time required, about 5 seconds if you type slowly.