Assuming the wiring is in good condition, yes, you will need a higher output alternator. Everyone thinks that LED's are super efficient and don't draw anything, and for the light output, they are efficient. However, they still use juice, the bigger the bar, the more juice they use. The 20" double row on my truck uses about 14A. I'd never have thought that it'd draw that much but it does. Verified via DVOM.
Now then, the wiring. Simply bolting a 40a alternator to the engine will help, but it won't solve the fact that the original wiring is pretty poor. Even brand new they were barely adequate. At the minimum, you're going to want to replace the factory charge wire to a 10ga or even 8ga wire. If I were doing it, I'd replace the external regulator, and install a newer style alternator that is internally regulated. Much more efficient-and generally speaking they last a long time. Very reliable. Put it on a 60A fuse. Just did this same deal on my G1900, to replace the original junk wiring and regulator. Could not be happier with the outcome.
You were testing at 1000 RPM? That's not even rated engine speed. What's it doing at rated engine speed (full throttle governed RPM)?
As stated, if you're trying to run the light bar off of the original wiring, that's no bueno'. The original wiring is pretty sorry, even if it were a brand new OEM harness, it's still poor, IMO. At the very least, the suggested relay should be considered mandatory, with it's own dedicated wiring directly off of the battery or starter (through a fuse or breaker of course).
