Keef
There was something wrong with that slaved HSI/DO you had if it could not follow heading changes quickly.
Normally these are gyro instruments so they respond like any gyro DI to heading changes, i.e. immediately. The slaving part of it merely updates the heading very slowly (a few degrees per minute or so) from a fluxgate magnetometer (a crude form of solid state compass) mounted usually in a wingtip.
I think the total cost of a slaved HSI system is nearer to 10k than 5k. But once you have a slaved HSI you can add a slaved RMI for a mere 4k
The same heading signal can also be used to rotate a gps and a stormscope display, etc.
This stuff is ludicrously expensive for what is actually in there.