Yeah, newguy, the C&V hivemind needs to understand why you want to modify this particular bike in this particular way.
Sounds like you want mountain bike features, and a speedster certainly does offer the solid frame. Bars can probably be done without much trouble (at max with a stem change, though you have to know that Schwinns use a less-common smaller stem size).
Tires may present a problem in that this model used weirdo Schwinn proprietary-sized rims (out of lovely chromed steel that can't be stopped in the rain). So you might need new rims/or wheels.
By this time, you have put a lot of effort into changing a bike in order to get features that could be had directly just by buying a different bike. And you've contributed to the entropic destruction of (what I presume is) another perfectly good originally equipped classic American bike.
I don't begrudge you setting up your bike the way you want it. I just would like you to ask yourself if the speedster is the right platform for getting what you want.
Eric