Henry, lots of people have chimed in with good tips for you, and certainly using Alan's batting lisp routine will work well. However, there is another option that you may find useful: individual object linetype scaling. I do this all the time for linetypes that are out to lunch in terms of the scale of my drawings.
As has been suggested, always draw at 1:1. I'm assuming you're plotting from paper space using viewports. Set your overall linetype scale to plotted scale if you won't be plotting in more than one scale. This way, most of your drawing geometry will have correctly scaled linetypes. Then select the linework for your batting and give it its own scale factor relative to the overall linetype scale. That's it, you're in business. The only drawback to this method is you may need to remember that you have some objects in your drawing that are individually scaled.
Unfortunately, because AutoCAD is somewhat hopeless in terms of handling scales of different base units, particularly within the same drawing, you'll find some predefined linetypes that are out-to-lunch in your particular drawing. If the linetype was defined with inches in mind, and you're drawing in feet, for example, you'll find that the linetype will not scale correctly. That's why, for instance, you'll find two separate linetype definition files come out of the box with AutoCAD - one for imperial base units, and one for metric.
Frankly, drawing scale handling is one of my biggest pet peeves with AutoCAD. Up here in Canada, where we use both imperial and metric scales on a regular basis, I often have to re-scale the actual geometry of drawings that need to be converted from one base unit to another - a huge headache that Autodesk should have dealt with ages ago. You'll find the same problem going between inches and feet as base units. As a result, some linetypes will have scaling problems. And then there's dimension styles - don't get me started.....!
Of course, if you're really handy, you could go into Acad.lin and add a definition of the batting linetype that would work in the base units you're using. It's tedious and a slight learning curve, but I've had success with a number of linetypes I've added for my personal use. Good luck!