Follow the manufacturers recommendations. Why risk it.

No big enough. You need a 40 amp circuit.
8.0 Kw @ 240 volts is 33.333 amps.
The specs should include a circuit size if read further.

"Other Requirements: 40 amp grounded outlet "

Equipment must be installed in accordance with the manufacturer's instructions.

"Other Requirements: 40 amp grounded outlet"

Is the oven 120V/240V, or just straight 240V? That will determine if you need 8/3 or 8/2 cable.

Thanks for the feedback! The specs from that Sears site are backwards it looks like. It certainly would be 33 amps at 240v, so a 30 amp breaker won't work.
I wish we could run 8ga wire to the oven location, but it's not a possibility. Sure would open up more double oven options for me!

In my shopping, I'm still surprised that some specs call for a 40amp outlet, even though the calculation of max Amps (Watts divided by Volts) equals less than 30 amps. (ie some ovens are max rated at 6700 watts @ 240v = 28 amps, but the specs still call for a 40 amp outlet.) Is there something I'm missing here?!
I don't want my 30amp breaker tripping all the time if I'm miscalculating, but it would sure be nice to have some other oven options than what I'm currently looking at.

There is a safety "fudge" on electrical rating of 20%. If you are over 80% of the usage rating, they round up to the next standard size. You don't want to put anything on a circuit that is going to continually push right up to the limit.

"I wish we could run 8ga wire to the oven location, but it's not a possibility"

Not sure why you say this, but where there is a will (and some money) there is a way.

Normally there is a minimum 40 amp circuit installed for a stove. Only a separate cooktop or separate oven will use a 30 amp circuit. Combine them into a range or double oven and you will need the 40 amp circuit.