Since 2 diffrent electricins verified that wiring harness of ur bikes are in good condiiton & as u told that light assy/housings are alos original & in good condition. so it seems me like generator/Alternator coil of ur bike is weak & its quite common problem with bike having old 6V electrics. If these coil are weak than installation of relay will not increase performance. So to verifiy the condition of generator coils, ask ur Electricians to directly put Headlight beam (Direct from Bulb Holder wires) to direct cable coming from generator coil if its glow properly than the problem is in wiring harness other wise Coil is weak & u shud replace it with new one ( in worst case ucan get it rewind).
Also let me tell u that if u simply get modify ur old setup to 12v ( by replacing Rectifier, Baterry & rewinding of coil as Electrician told u)it will not gives u better results( like u want same as in brand new bike) & in most of the cases it becomes mess.
So i wud say again that its better to stay with original setup (After proper repairing) or other wise switch to complete 12V setup including Magnet new 6 coil genreator plate & original CDI system if u want results like new bikes.