I think the 5L pump has a 10mm plunger and the 1KZ pumps have 12mm. So 5L will flow less fuel. Also, check the rated injection pressure (part of the VE part number) to see how it compares. Might have to re-shim the 1KZ injectors to match the pump pressure? You'll need to source a boost compensator to increase fuel with boost pressure. I think I've heard that the cam plate in the pump is similar between the L and KZ series, so when you time the pump, you can probably use the 1KZ specs.
A the end of the day, you'll probably be making less power no mater what. I think the 5L pump maxed out will only make about the stock power of the 1KZTE.
Why don't you sell your 5L injection pump and buy a 1KZT pump? Or get an auto electrician to fix your electronics. Probably just a matter of cleaning/drying connectors.