overthinking the rules really. feel free to do anything you want as long as you try to do it cheaply. then there will be a poll and the people will decide if they like it or not. some of that will be back story on how it all came together- so taking an old rusty frame out of a ditch and scrounging parts and paint will probably get you more props then "I found this perfectly usable bike in the thrift shop for $10 then rode it 10 miles home".
on the other hand, awesome thrift shopping does deserve shop props, so enter it!
and for counting up the cost, just put in the description things like: "wheels i got off a bike i bought for $10, I consider them about 30% of the value of that purchase, so lets call it $3.33"