Dash out... Seems familiar somehow...Cant think why.do you know the cause of the burning? That would be the first mission: to establish why, the last one went on fire, we do not want a repeat performance!
Id go for replacing wires and using heatshrink where possible, if not heatshrink then self amalgamating tape. Electrical tape is ok until the adhesive gives up or it turns to a gooey sticky mess and falls off anyway.