You should be able to drag and drop the styles into the template. If you have the drawing open with the styles you have updated and you then open the dwt (SDI needs to be set to 0). In the drawing area, minimize the your dwg and the dwt should be in view. The drawing (or dwt) that is currently in the drawing area will be the one current in your toolspace (bold). Go to the toolspace and find the dwg and expand the pluses to get to the style you want to drag - drop. You can now drag it into the drawing area or through the toolspace to the appropriate place in the dwt's list of styles and drop it there too.
Another way I have done it is to get my drawing going, update or change the styles and some layers here and there, then save the drawing. After the save do a saveas to a dwt file. I overwrite the old dwt (be careful though). This way you will not miss a style, layer, dim style, text style, etc. that you have created in the dwg. Hope this helps.