You can do the change if you want. Or, perhaps consider some treking bars. It may be better to just find a cheap road bike or cyclocross bike.

The cost adds up quickly. You may need:

• Handlebars
• Possibly handlebar stem (keep in mind there are a few standards, 1" stem (22.2mm quill), and 1 1/8" (25.4mm quill) are common. You probably have the larger 25.4mm quill.
• Brake Levers (get a long pull such as the Tektro levers, or see notes on Travel Agent).
• Shifters (or integrated with the brake levers)
• New brake and derailleur cables and housings.
• Depending on the brake lever choice, perhaps also a "Travel Agent" to convert brake pull.
• Handlebar tape

What type of shift levers do you have in mind? I've snagged some stem shifters for cheap. They're functional. On my most recent build, I had some old Suntour stem shifters made for a 1" stem (22.2mm quill) which I was able to barely coerce onto a 1 1/8" (25.4mm quill), but I seem to run into lots of problems mixing and matching old and new stuff.

Are you in Portland?