Where do I find 4-4-4-6 direct bury copper cable?
That choice of copper wire is going to be even more expensive when the inspector makes you rip it out and replace it with the 3-3-3-5 you should be using.   You need to use the 75C column in 310.15b16 and can't use the 83% bonus derate on subpanels.

There's an urban myth that 4Cu/2Al is allowable on 100A, that was due to a misunderstanding of the applicability of 310.15b7, which in fact only applies to service entrances that serve the entire dwelling unit.  E.g. from meter to weatherhead or from main shutoff to main panel.   NOT subpanels.  

I agree SER is not made for direct burial. 

I concur that at this distance, 3Cu or 1Al will contain voltage drop to &lt;3% at 60A.  Expect about 4% at a full 100A, which I wouldn't lose any sleep over.  You are correct not to design for 3% at breaker trip current.  

Regardless expect to spend $5-7 per foot for #3Cu and about $1.60-$2.00/foot for #1Al.  

The price you will really pay is decided by your local electrical supply house, at least the one willing to carry oddball cable like this.   The size isn't oddball, the use of copper when just about anyone else would use aluminum is oddball.  

Some houses in the 1970s had a problem with 15/20A circuits using powerline grade aluminum (AA-1350). But there is nothing wrong with aluminum feeder at #4 size and up, even the obsolete AA-1350 alloys proved reliable.  Regardless, out of an abundance of caution, AA-1350 was outlawed and a new alloy, AA-8000, was invented specifically for household wiring.  The lugs will be aluminum, which means aluminum feeder does not introduce a "dissimilar metal" issue - but copper does!   Ironically. 

Given your desire for copper, you are probably better off laying conduit e.g. sched. 80 PVC, and running individual copper wires (THWN or XHHW) therein.  They definitely   make those in copper.  The downside is theft risk, but it's a lot harder to steal buried cable.