I had the unfortunate experience of something similar with my EFI Baleno. The car won't start at all even after 10-15 selfs. After applying the process of elimination on a few susceptible culprits I decided to check and see if petrol was getting to the FI rail, right after the intake manifold/throttle body. Turns out the fuel pump was acting up and would fail every now and then to send petrol from the tank to the fuel filter and into the injection rail.
You should check if this is the case when the car is cold. Switch the car to petrol. Remove the outgoing tube/pipe from the fuel filter (the one that feeds the carburetor) and turn the car on with the key. When I say on, just turn the key to right before the self point, i.e. when all the lights, etc, light up in the speedometer display. Now, the pump should start pumping petrol from the tank, through the filter and out the disconnected pipe. Have a pepsi bottle handy to catch any petrol that comes out. This should give you a fair idea if the fuel pump is the culprit or not.
About the electrician checking the fuel pump, did he do that with or without removing the fuel tank? I had to get the tank removed and the fuel pump replaced to get the problem resolved. If there is not enough fuel gushing out the fuel filter you might have either one or both of following problems:
1) Defective pump. Works intermittently and dies every now and then.
2) Fuel filter is choked.
If the symptoms persist after resolved/checking the things above, your carburetor might need some fine-tuning. Getting work done on the head is totally unnecessary and is a huge rip-off. Run from the 3S mechanic as fast as you can. Hope I was helpful.