This answer is not the most-specific for the user's question Please see my 2nd answer. I am leaving this here because it addresses the more general issue.
Per the comments to your original post, you need (1) a terminal emulator which supports bracketed paste and (2) corresponding support for whatever is running in the terminal, ie,
zsh. Terminal emulators supporting bracketed paste (list to be updated based on comments to this post):
xterm - since ??
gnome-terminal - since ??
putty - since 0.63 (2013-08-06 release date)
Applications supporting bracketed mode:
bash, StéphaneChazelas has put together a shell script to facilitate the detection of that mode and take appropriate action.
A more specific answer -- preventing lines from getting chopped off -- is unanswerable without knowing about the unix program that is running when you hit paste.
A clipboard manager maybe what you need.