In any case, you need a new or repaired steerer. So, see to it the new one has threads that stop much further up. One or two usable threads below the headset, not 13 plus. You could also lower your current stem several millimeters simply by using a thinner lockwasher in the headset (which includes most ever made so you have lots of choices).

As said above, the expander in you stem MUST be below the threads. (It's also a nice safety feature. If the steerer ever does break again, your stem at that expander is keeping your front wheel attached to your handlebars, giving you limited but enough steering and lowering the heart rate peak substantially. You didn't say but I'd put money down that you experienced quite a spike even if you didn't record it.)

Edit: If I decided I wanted to go with a steerer replacement, I'd call Ti Cycles. Dave Levy has seen it all and knows many repair options and also when those options are poor choices. If he cannot do it, he'll tell you in that phone call. He's not cheap but won't take you for a ride. A replacement steerer will probably kill the paint but he may know a repair that can be done midway with the heat far enough away.