Hey brewerbob,
I have owned that same generator for almost the past 5 years. (however, mine runs on natural gas). They are loud, relatively cheap for a standby generator, and effective. We seem to loose power 2 or 3 times/year. Maybe we don't pay enough taxes in this part of Michigan, or maybe we are late paying our utility bills, I don't know. This is what works, and does not work so well:
1) I have no experience on Amsoil ASE. So I can't comment.
2) Castrol 0W30 (made in Germany variety) seemed to work the
best. Very little consumption power outages (15 hours).
Slightly less valve "clatter" noise according to my ears.
3) Straight 30 wt. Havoline worked well in a 30 hour 90F outage.
Some was consumed but the generator never shut
off due to low oil level. It was the first one I used after
initial break in. (I didn't know the outage would last this
long, otherwise I would have used a synthetic oil). Oil did
look real "beat up" and black as tar.
4) Mobil 1 0W30. I consumed almost 1/2 quart of the 1 3/4 qt.
capacity in about a 15 or 16 hour outage in 10F temperatures.
My generator did not quit, but I have heard of others, when their generator quit, having to refill the oil level using Mobil 1 5W30 after the oil level
got too low (it is a thin 30wt oil) in their air cooled
generators.
I am partial to Castrol 0W30 - if you can get it, for year round usage. I noticed you are in the state of Washington. If you can go across the border in Canada and buy Esso XD3-0W30, that would be a good bet. It, like the Castrol 0W30 are almost 40wt oils. I have some of that laying in wait, for the next big outage - whenever that is. I see no reason, Rotella 5W40 should not work effectivly. I am sure someone else who uses it will chime in.
I change my oil for summer & winter every 6 months (unless I loose power for extended periods in between). Also, the big tip, that I have picked up: The oversized Toyota Corolla oil filter, Purolator Premium Plus # L14477 is a perfect fit for this generator. With it, you can pour the full 2 qts, instead of 1 3/4 qts.