My 2 cents:
As a contractor, charge a lot. They either have budget and want to spend it RIGHT NOW or they don't. The manager engaging you doesn't really care about your daily rate (relatively speaking).
Above comments on automation is spot on. Test suites might be terrible, so the care required to make changes without breaking things is your responsibility, hence the slow pace. What is in your control is the ability to automate your own testing.
Integration with poorly defined APIs is an important skill. You generally won't have another team maintaining and improving a nice API. You will have access to obscure data stores dumped untransformed in the data warehouse from another megacorp's expensive and poorly documented product, possibly with myriad ETL nuances (read: bugs). Learn to work with this and you can extract gold.
If you have a Windows SOE system, embrace Cygwin/similar.
Curious if you have any tips for this stuff? My instinct would be to just poke and prod things, writing tests or documenting things as I go along. "I wonder what happens when I do X" -> write a test, get a result. "I wonder what data looks like here" -> examine it, write a summary of what I found. Etc.