Have you considered that the underlying cause of such an infestation is excessive use of nitrogen fertilizes of some type? Excess nitrogen attracts them in droves.

Never had such an infestation such as you describe as I only use very low dose N in small amounts. S o the water hose and just stripping them off with fingers works fine for me even with hundreds of plants. The lady bugs take care of the rest. Corn is the only crop I ever have any real issues with them because of all the high N feeding it requires. But both peppers and eggplants require minimal N.

I assume you know that Neem and Safer Soap can also kill ladybugs so could be reducing your natural controls?

Another effective way of controlling them is taped fingers (masking tape) rubbed up and down the stems lightly. Picks up hundreds at a time.

Then there is Surround, a kaolin clay dust used to control various sucking insects. Quite effective but messy to work with.

Otherwise about all you can do is bring out the big gun pesticides like malathion and permethrin which I never advocate doing. Do keep in mind that the majority of the damage done by aphids is appearance type and usually tolerated by the plants unless the infestation is quite severe.

You might use the search to pull up all the 100's of previous discussions about 'aphid control' on this forum for additional suggestions.

Dave

IPM Aphid Controls