Hi,
it's always difficult to be 100% sure without knowing more deeply the network, traffic types and patterns, what kind of devices are connected to it (sometimes the network upgrade can be fine but the end-systems don't like it) and some other configuration details.
However, on a generic level, I'd be confident that this should go smoothly. I have already run EAPS topology with 16.1 core switches and ExtremeWare edge switches, without an issue...
To start with, there's a 15.3.5.2p1-11 that has been recently released.
Speaking of EXOS version, 12.3 is very old. From the top off my mind, this release is a "pivot", I do recall there were many changes around it, and I do recall telling some customers to do a step upgrade to 12.6 before going to the targeted release. You'll have to dig into the RN but I think some default behaviors were changed (look for STP and VRRP mainly). Be sure to have a copy of the config unaltered by the upgrade process in case you need to rollback (simply do multiple copies of the config).
I believe the most critical part of your upgrade will be on the Core, as this is an EAPSv2 topology, I assume your Core manage a shared-link. While I'm not aware of any problem doing this upgrade, I'd test it if possible.
As for ELRP, since 12.3 the feature as been nicely enhanced (and is still in recent releases btw - ELRP is a very nice protocol). That shouldn't affect its behavior, but from 12.3 you'll have access to new parameters (like the ability to block a port automatically) that you may want to implement (after the upgrade process as I'd not recommend doing 2 different things in one MW).
Stephane