Most of the people on Pond Boss with smaller (0.5 - 3 acre) sealed ponds are what you have called "stagnant". Most of the year, these ponds do not have any water running through the outlet pipe. Fortunately, most ponds with healthy plant populations can readily handle that situation and can support large fish populations. Even so, there is a busy section on the forum covering "Aeration" for the ponds that need a little extra help.
Groundwater ponds like yours do not allow quite as much control for the pond owner. If your pond has a good connection to a permeable groundwater aquifer, then I think it is very unlikely that you can pump enough water to raise the elevation by a significant amount. I think the hydrostatic forces will readily push the "extra" water right back down into the aquifer.
However, changing the chemistry of your pond water may be a slightly easier task. The main movement of water from your pond should be evaporative losses that are then replenished from the aquifer. Since only the water molecules are leaving, any chemical species that you add to the pond MAY have a significant residence time, and it may therefore be possible for you to economically alter your water chemistry.
Unfortunately, the groundwater in some aquifers may move very rapidly. This is more likely in areas with greater slopes, very permeable sand/gravel aquifers, or places with a continuous removals of water (like a river at the lowest surface exposure of the aquifer). I don't know how many of those variables apply to your groundwater pond.
I think I would start by following the advice of jpsdad and Bill Cody and see how much you can first improve your bass fishery by sampling and culling as needed. Only after several years of diligent work with poor results, would I then contemplate spending money on changing the chemistry if that appeared to be part of the problem.
Good luck on improving your fishery! It sounds like you have an excellent start.
