In the release notes for Junos 12.3 (http://www.juniper.net/techpubs/en_US/junos12.3/information-products/topic-collections/release-notes/12.3/topic-69605.html#pre-resilient-dual-root-upgrade-ex) on Juniper EX series switches, it says:
Upgrading from Junos OS Release 10.4R2 or Earlier
To upgrade to Junos OS Release 12.3 from Junos OS Release 10.4R2 or earlier, first upgrade to Junos OS Release 11.4 by following the instructions in the Junos OS Release 11.4 release notes. See Upgrading from Junos OS Release 10.4R2 or Earlier or Upgrading from Junos OS Release 10.4R3 or Later in the Junos OS 11.4 Release Notes .
Unfortunately, Juniper don’t list any Junos releases older than 12.3R1 for the EX4200 (and possibly other EX series) on their download site.
After poking around the Juniper support site for a bit, I found technical bulletin TSB16151 (https://kb.juniper.net/InfoCenter/index?page=content&id=TSB16151), which contains downloads for Junos 11.4R8-S1 on EX2200, EX3200, EX3300, EX4200, EX4500, EX6200, EX8200 and XRE-200.
With this and the jloader files from technical bulletin TSB15524 (http://kb.juniper.net/InfoCenter/index?page=content&id=TSB15524), I was able to complete the upgrade successfully.