Problem when using GNU Screen 'stuff' command with 40+ open tabs - runaway input to stdin

Once a month I conduct system diagnostics on about 40 machines at an IDC for a Korean food company. Because the commands I need to run (i.e. dmesg | grep -iE "criti|fail|warn|bug|") are the same for all  machines, I use a script to launch GNU Screen with dozens of tabs each ssh'ing into a different server and once connected to all machines, I use

C-a :at "#" stuff "cmd^M"

to send commands to all tabs at once. Without this feature, there is no way I could complete a system checkup on 40+ machines in less than a few hours.

I recently had to install the leap second patch for tzdata packages on 40+ RHEL6.X machines, and wanted to scp them from my local machine to all the servers in one fell swoop. Therefore I entered the following command into GNU Screen:

:at "#" stuff "scp -r archjun@10.200.250.156:/MULTIMEDIA/iso/pkg-update/tzdata^M" .

As this was a new ssh connection, I was prompted whether I wanted to continue connecting:

The authenticity of host '10.200.250.156 (10.200.250.156)' can't be established.
RSA key fingerprint is
...
Are you sure you want to continue connecting (yes/no)? yes
Warning: Permanently added '10.200.250.156' (RSA) to the list of known hosts.
archjun@10.200.250.156's password:

Obviously I wasn't about to type 'yes' into each of 40+ tabs. Therefore I stuffed yes into all 40+ GNU Screen tabs using

:at "#" stuff "yes^M"

All was fine for about 20 tabs, but the remaining tabs entered an input loop stuffing an infinite number of y's to stdin

y
y
y
y
y
y
y
...

In my .screenrc config file I have automatic logging turned on with the two lines

logfile $HOME/Documents/term_sessions/%Y-%m-%d_%0c-%n.log
deflog on

so that a logfile is automatically generated as soon as a new GNU Screen tab is created (hotkey C-a c). I noticed that logfiles were suddenly ballooning to hundreds of megabytes in size.

I manually had to enter C-c into each of these tabs to stop the runaway input. I have never experienced anything like this when stuffing commands to all windows in GNU Screen. Has anyone else encountered similar behavior?