Hi Mass,
Do you have console access of these devices? If yes then you can do as below
1) You can install Junos on both devices without reboot ==> request system software add no-copy no-validate <path of package>
2) After installation, halt node 0 => request system halt
3) Once node 0 halted, then you can reboot node 1 ==> request system reboot
3) Once node 1 come back in 12.1X44-D35 version, make sure all good and then you can boot up node 0 by accessing its console and hit enter.
4) Node 0 will boot up with 12.1X44-D35 and join the cluster.
Yes, 12.1X44-D35 should be stable release.
Thanks,
SHKM