Pull the mast or not
I agree that using the halyards as temp. backstays to be the easiest answer. Recently while relpacing rigging on my deck stepped Columbia, we were able to create a bridle around the aft cleats and attach main halyard to the bridle. I cranked down on the halyard, taking some of the strain off of the backstay. I should add, I have a end of boom mainsheet and tightened it down as well. It pull against the topping lift, creating another temp. backstay. The mast never wiggled. Using the jib (and spare jib)halyard to the forward cleats allowed the same setup to work on the forward rigging. Good Luck.