Curiosity got me to look at your clip and just by running the Acapella filter I was able to lessen the room ambiance. Some coloration appeared but EQing helped with that. Give it a try if you haven’t already.
You don’t say how large the files are but video is usually large as in Gigabytes per hour of footage.
USB Flash drives are expensive and without a lot of capacity.
You may want to consider a portable hard drive that runs off of USB2, that means no AC adapter. https://www.newegg.com/Product/Product.aspx?Item=N82E16822136228
I’d render the full production out to your native format (DV, HDV or whatever). The same format you started with, it will be lossless (no loss of quality). Then take that new file back into Vegas and cut. Then render out to Mpeg2 for DVD’s.
The idea is to render as high of a bit rate as will fit on the target media. A bit rate calc helps in that regard. Audio has to be factored in with it also.