We switched to nginx-rtmp temporarily (version 1.6.2 from nginx-extras in dotdeb) and it still had the corruption/stuttering thing, but only in very specific circumstances on specific networks.
However, as an accident, upgrading the entire wheezy system with wheezy-backports repo (apt-get -t wheezy-backports dist-upgrade) made it stop happening on nginx (confirmed on 2 reproducible cases i’ve had on 2 different servers), , so maybe it will solve this problem for any other evostream users on wheezy stable (the upgrade brought the kernel from 3.2.0-4-amd64 #1 SMP Debian 3.2.60-1+deb7u3 x86_64 to 3.16.0-0.bpo.4-amd64 #1 SMP Debian 3.16.7-ckt2-1~bpo70+1).
EDIT: Confirmed, rebooting with the older kernel (3.2.0-4-amd64 #1 SMP Debian 3.2.65-1+deb7u1 x86_64 GNU/Linux) brought back the stuttering/drops. So avoid this kernel for RTMP streaming.