[captlar]

I assume you mean the halyard does not run free when mast is upright. If the mast is in the rack, you may not even have a problem once the mast is in the boat. I have replaced many halyards in the rack and often they will not run freely.
If you have the mast base removed, I assume the stick is not in. Just attach a string to one of the halyards that is running free, pull it through and fish it over (thin wire) to appropriate plate and sheave. Attach (or reattach existing if in good shape) new halyard and all done. Not so bad. Good excuse to skip work for a day.