Hire a consultant to do a full-memory dump.
1. That gives you a pretty good chance of attaching a debugger (to the offline memory file) and extracting the config from memory without touching the running system.
2. You are safe in case things turn awful, which seems likely.
As for the source code, if it is an interpreted language like Java or Python or C#, your chances of recovering a fully-working source code tree are pretty good. At the very least, it'll help with understanding what the system does.
For C / C++, buy Hex-Rays IDA and Decompiler. That's what the pros use for reverse engineering video game protections, breaking DRM, etc. So that tool set is excellent for getting a overview of what a binary does with the ability to go into all the nitty-gritty details if you need help re-implementing one detail. Plus, Hex-Rays can actually propagate types and variable names through your disassembly and then export compile-able C source code for functions from your binary.