Hi Hartr,
I think we should try another option instead of Client template.

Client template can't work like quick message.because client template are table specific and only default only one template show when click on email icon. so there is no multiple option for client template.
If you want to select multiple option for email template then create one choice filed on any form and specify template name.
another thing if you want to see which template i am sending then make one custom field like Email already send. when select any template from choice and click on UI Action then send template choice value are save in Email already send.
Note: If select caller then caller email auto populate and send template. if caller are not available then optional caller name and caller email address use and then send email template.

Step 1: create choice field and name like Template after that right click on template field then personalize choices after that create option as for your requirement and save. again right click on Template field and click on show choice list then you will find label and value in list mode.
Notice: value of choice field and event name must be same.
example: value-> misscalltemplate
event name-> misscalltemplate
so create event as same of choice filed value.

step 2: Create email template as for your requirement
step 3: Create one UI Action like Send Template
Name: Send template
Table:..........
script:
if(typeof window == 'undefined') {
semail();
}
function semail(){
var e='';
if(current.caller_id == '' ){
e = current.u_email;
} else {
e = current.caller_id.email;
}
gs.eventQueue(current.u_template, current, e, 'Email');
if(current.u_emails_already_send==''){
current.u_emails_already_send = current.u_template;
} else {
current.u_emails_already_send = current.u_emails_already_send+"",""+current.u_template;
}
current.u_template = '';
action.setRedirectURL(current);
current.update();
}
step 4: Go to notification and make new notification.
Name : Notification Name
Table : ......
when to send:
Send when: Event is fired
Event Name:select event name

Who will received
Event parm 1 contains recipient: check ( Note: No need to select User/Group in the field because i have two caller one are optional and one are user table caller )

What it will contain
Email template : Select email template and save

I hope you can select multiple template from one table and easy way send and to see which template are send. it will show in text box.
Kind Regards,
Chandan Shrivastava.