Receiving larger data from the Serial interface

Hi all,
in my project I am receiving with the Yun a datastring via Serial interface (software serial, beacuse the Serial1 is used by the bridge) and sending it to a server. Everything works fine so far. But how to deal with larger data (about 4 KB)?

Collecting the data in a String or char-array will not work, because of the 2.5 KB SRAM limitation.

Sending the data synchronously to the server will also not work. This takes time and the arriving serial data will not wait.

Storing the data on SD-card will not work because of the same reason (Writing to card from the aruino side is using the bridge and very slow).

Other ideas I don't have. Can someone help me?

for big size file please bypass FileIO at ATmega32u4 , let AR9331 take care it only.