Just tested Clipmate. Opened the Clipmate window showing the desired list of clips, selected the desired clip (all you have to do is select it) and pasted it into the title of a TDL task, no problem. Can paste it as the full title, or add the clip before or after the already existing title.
Clipmate also has other amazing ways of doing things like this like 'QuickPaste' and 'PowerPaste' into other apps, but have not tried this with TDL. But now that you bring it up, I may just experiment with that to see if I can think of some helpful ways to use it!
This was a virtually unknown app. Little publicity. But I've never seen another clipboard manager that even comes close to its powerful features. Can't guarantee anything since it's been so long out of development, but might be worth a try if you think it might help. I have a select few apps that I launch on startup and always keep running in the tray. It's not easy to make the cut. But Clipmate is right up there on that list.
We all know that some of the least publicized apps sometimes turn out to be the best! I love finding the gems in the weeds.

===NOTE===
Did you see somewhere that Clipmate is now free? Just took a quick look at the site and didn't see that.
The download may be a trial.
If you don't want to be stuck with the trial, might be a good idea to attempt to contact the developer (not sure if you can) to find out the deal before installing it. I used to be in communication with the developer suggesting ideas and doing some testing, but have not had any contact for at least maybe 15 years or more and have no idea if you can still reach them or not.
Not sure if it will function sandboxed. I used to sandbox everything but now I have a different strategy to protect my system.