Thank you for the excellent answer!!
Regarding the 30A breaker only being good for ~6500 watts, moving up to a 40A is a simple fix, and the 8/3 wire would handle that load. However, if the generator's breaker is 30A, would increasing the size of the feed breaker in the panel make any difference?
I saw this thread come up in the pingbacks on Norwall's blog. Since I wrote that post, I thought I'd respond.
First, the lockout breaker you are using is a two-pole connection. It does not switch the ground or the neutral wires. The portable generator's frame should not be bonded to the neutral. Only one bonding point is allowed and that permanent connection is already made in your home's panel. Most manufacturers provide instructions for bonding or not bonding so check your manual.
Regardless of your lockout breaker size, you are limited by the outlet capacity and size of the breaker on the generator. If you're connecting the inlet box with a cord to the 30-amp receptacle on the generator, the generator receptacle breaker will trip if the current exceeds 30 amperes. Further, if you bought the cord for a 30-amp receptacle, more than likely it is only rated at 30-amps.
There is a problem going to a 40-amp breaker however and maybe it's not quite so obvious. The inlet box is rated at 30 amperes and the wires are rated for 50 amps (assuming 75 C insulation). Suppose you up the lockout breaker to 50 amperes. Later you sell the house. The next owner sees the 50 ampere breaker and assumes (wrongly) that the entire connection is good for 50 amps and they rig a cord to connect a 50 amp generator outlet to the inlet. The connection now poses a definite risk of fire because the inlet box was only rated at 30 amperes.
So no. Don't change the lockout breaker size to anything greater than 30 amps.
This is also why you never use a smaller gauge wire on a circuit just because you're only powering a light socket. If you have a 20-amp circuit, don't think to get by with #14
to connect a light socket. The next guy may come along and plug a 2200 watt heater into that socket and the wires are only rated for 1800 watts (15 amps).
A generator rated at 8000 running watts will supply a continuous 33 amps at 240 volts. Don't worry about those 3 amps. The 30-amp outlet and breaker on the generator won't allow you to exceed the 30 amps anyway.
Remember. Turn off the power when you make changes to your electrical system. If you don't feel confident or don't understand what you are doing, call an electrician.