Forgive the rudimentary explanation but this is the only way I can convey my suggestion...
When the tap is in the "on" position the fuel is being supplied through a tube which extends upward into the tank. Once the fuel level falls below the the top of the tube fuel can no longer enter it, so you have to switch over to "reserve".
As I see it, extending the bike's range before having to switch to reserve would require removing the filter from the tube, and shortening the tube thereby allowing fuel to continue to enter it at a lower level. Of course you would need to re-use or replace the filter.
If it were me I would remove the fuel tank from my bike and fill it completely with fuel, then turn the tap to the "on" position and measure the amount of fuel supplied from that position. I would then switch to "reserve" and measure the remaining fuel. I would then trim the height of the tube in very small increments, repeating the process of measuring the fuel supplied in the "on" position until I reached a reserve amount I was comfortable with. I don't think I would go below 3/4 of a gallon of reserve fuel, and of course it would be prudent to know how far you can ride on your reserve supply.
See the pic below, which I believe is a Bonneville tap but if it's not it's close enough for the purpose of illustration...