Not sure as to whether or not they support Linux, but...
Lynx Studio AES16e-SRC and AES16e-50 both utilize the very good Texas Instruments (Burr Brown) SCR4392 asynchronous sample rate converters on the inputs (the -50 version adds AES50 I/O via an internal connector, but is otherwise similar to the -SRC version). Utilizing that asynchronous sample rate converter functionality would allow a different sample rate at the input port and output port by converting the sample rate of the input stream to the different sample rate used internally, and the internal sample rate is what is used on the output.
The biggest downside is that these are not RME products with RME's excellent drivers, support, and the very capable TotalMix. The Lynx mixer used with the AES16e family of cards supports only 32 channels.
Here is some information about the SRC4392, which is very good at what it does.
TI product page: http://www.ti.com/product/SRC4392
TI data sheet, pdf: http://www.ti.com/lit/gpn/src4392
Additional info related to the evaluation module: http://www.ti.com/lit/pdf/sbou038