I think doing either set_case_analysis or set_dont_touch_network have some possible issues
1. If with set_case_analysis, there may be some unwanted optimization in the fanout of the "master control signal". If it's really static, why not change it to a constant
2. If with set_dont_touch_network, the logic in the fanout may not get mapped to gates (remain as GTECH cells)
I suggest the following options
1. No extra constraints. Just let DC treat it as single cycle timing from the "master control signal"
2. If it fails timing, I suggest add a set_multicycle_path. Just remember to also set properly for hold timing (e.g. if mcp_setup = 3, use mcp_hold = 2), and ensure the "master control signal" is really stable before the rest of the chip operates.
3. If this signal is heavily loaded, you can add a set_ideal_network (you can also use -no_propagate option), and then let the backend guys insert the buffer tree
Hope these help