I own a 93 accord wagon and had to pull apart the abs/brake system to refurbish the abs pump, this worked well and the abs light is now off. This required pulling apart some of the brake system and having to flush and bleed the brakes and abs modulator. I also primed the abs pump by jumping the abs relay 5-6 times for a few seconds.

First, the brakes were bled in order, and there is no air coming from the lines. Second I bled the abs modulator. The abs modulator is a little more difficult, as I did not have the bleeding tool. I extracted as much liquid as possible and refilled the reservoir twice, the liquid was initially foamy, however became clear.

Pumping the brakes when car is off and then pressing for a long period of time does not cause the pedal to drop to the floor.

The brake pedal is very tight when the car is off, however becomes softer when the car is turned on. This leads me to believe its the abs system causing this diminished braking ability. Is the pump/modulator adding air to the system?

The brakes were never as tight on this car compared to other honda's with a similar vintage; however according to my dad the brakes are now softer than before.

 

You can also bleed at the master cylinder as a final bleeding point if you are concerned of it being a bleeding issue. My CD doesn't have ABS so i can't speak to bleeding at the abs pump but maybe someone else can

I would say try re-bleeding the entire thing again, a lot of laour, but not much expenditure on fluid, at least you can rule it out