Mea culpa! I really should have mentioned that.
The AWS instance has 32 Gb RAM and a Quad-core CPU. It has 4 SQL instances running on it. The instances are memory-capped as follows:
2048 Mb (our problem child)
for a total max 30548 Mb usable by SQL, leaving a minimum of 1.5 Gb RAM for the OS.
Believe me, I am thinking long and hard about moving off SQL Server, at least for this particular DB. Unfortunately, that is a major architectural and development project. All my instances work with each other, they've been SQL Server since before SQL 2000. Never had a problem with this.
I am not aware of any throttling on AWS end, besides, both the server and the client are in the same AWS subnet, so their data exchange is internal to that AWS subnet.