Thanks to the many and varied responses, I have a lot of options.
Back in the 88 time frame I engineered some Ford export parts that including wire harnesses that went to New Jersey for installation. It was a relatively small business (~90 people) as far as Ford suppliers go. We had a semi automated crimping machine. The terminals were spooled in batches of 1000 or so. The wire was stripped manually (remember the low volume comment), then inserted by hand into the die. A foot pedal brought the dies together to crimp and cut the terminal, and index the terminal for the next crimp.
In my case I had planned on tinning the wire, crimping (I have a few types of crimping tools, but nothing as good as what I mentioned above with a specific die to match the terminal), then a final hit with some heat and more solder if needed. Sinking the heat away from the insulation is good, as Jim mentioned. If you don't have a hemostat, you can use a small C clamp or vice grips with swivel pads. Obviously in any case be careful not to bear down too hard.
I don't think there is an overheating concern as long as the workmanship is good (no cut strands, everything cleaned up, etc.) Since the terminal is in a black plastic protective sleeve, I don't think it will be seen, making looks secondary in this specific application. Other applications could be a different story.
Regarding Bob G's suggestion I've used that on other projects, and agree that staggered splices is the only way to fly under the radar.
The "new" idea for me anyway was Richard's suggestion to cut the wire off the donor and drill out the old wire. After than I can use varying sized of picks to pry them open.
Thanks again.