The trick is to find out what line to begin on. If you happen to know this, then you can just copy and paste your program start lines and insert it into the program at the proper position. Then do a program search to find this new start point.
Make sure that the proper tool change has been accomplished.
Give yourself a little leeway by starting a bit earlier than you need to. If you can single step for a while in DNC mode, this would be advised, with the Rapid override turned way down. Once the tool looks like it is approaching the right pathway, then you can open the feed back up
you could draw a new boundary over your part representing where the machining needs to continue, and generate a new program, just as though it were "Rest machining".
Give your spindle a few minutes of run time to warm up before you begin the cut.