Why are you aerating? What's the objective?

I'll see how it is in the spring but I think there's some compacted soil.

Also it was recommended by Rutgers, but they said May.

Have you sprayed with shampoo? 3 ounces per 1,000 square feet?

I did try the shampoo. I did not see or feel any difference.

Is it worth doing this time of the year? Or wait until Spring?

Yes, do it any time. Spray it on and water it down with 1/2 to 1 inch of irrigation/rain. I would give it 3 full weeks to improve. You should see it only when the soil is moist. Then the soil should become soft. If it does not feel softer after 3 weeks, repeat a time or two. It should become softer each time (as reported on another forum by people who have done it).

I've been trying shampoo in a hose end sprayer the last few weeks. It really works. Can't hurt anything, it's not critical that the amount is closely monitored. Give it a try. It seems to improve water uptake or utilization and retention. I suspect insect pests don't appreciate it either.

Any burden to soil microbes?

None. I spray baby soap along with kelp, humic acid and pinch of blackstrap molasses every couple weeks during the growing season.