How to avoid distance ordering in large scale billboard rendering with transparency - c++

Question

Setting the scene:
I am rendering a height map (vast non-transparent surface) with a large amount of billboards on it (typically grass, flowers and so on).
The billboards thus have a mostly transparent color map applied, with only a few pixels colored to produce the grass or leaf shapes and such. Note that the edges of those shapes use a bit of transparency gradient to make them look smoother, but I have also tried with basic, binary color/transparent textures.
Pseudo rendering code goes like so:
map->render();
glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
wildGrass->render();
glDisable(GL_BLEND);
Where the wildGrass render instruction renders multiple billboards at various locations in a single OGL call.
The issue I am experiencing has to do with transparency and the fact that billboards apparently hide each-other, even on their transparent area. However the height-map solid background is correctly displayed on those transparent parts.
Here's the glitch:
Left is with an explicit fragment shader discard on fully transparent pixels
Right is without the discard, clearly showing the billboard's flat quad
Based on my understanding of OGL blending and some reading, it seems that the solution is to have a controlled order of rendering, starting from the most distant objects to the closest, so that the color buffer is filled properly in the end.
I am desperately hoping that there is another way... The ordering here would typically vary depending on the point of view, which means it has to be applied in-real-time for each frame. Plus the nature of those particular billboards is to be produced in a -very large- number... Performance alert!
Any suggestions or is my approach of blending wrong?

Answer 1

Did not work for me:
#httpdigest's suggestion to disable depth buffer writing:
It worked essentially for billboards with the same texture (and possibly a specific type of texture, like wild grass for instance), because the depth inconsistencies are not visually noticeable - however introducing another texture, say a flower with drastically different colours, will immediately highlights those mistakes.
Solution:
#Rabbid76's suggestion to use not-semi-transparent textures with multi-sampling & anti-aliasing: I believe this is the way to go for best visual effect with reasonably low cost on performance.
Alternative solution:
I found an intermediary solution which is probably the cheapest in performance to the expense of quality. I still use textures with gradient transparent edges, but instead of discarding fully transparent pixels, I introduced a degree of tolerance, for example any pixel with alpha < 0.6 is discarded - the value is found experimentally to find the right balance.
With this approach:
I still perform depth tests, so output is correct
Textures quality is degraded/look less smooth - but reasonably so
The glitches on semi-transparent pixels still appear - but are nearly not noticeable
See capture below
So to conclude:
My solution is a cheap and simple approximation giving less smooth visual result
Best result can be obtained by rendering all the billboards to a multi-sampled texture resolve with anti-aliasing and finally output the result in a full screen quad. There are probably to ways to do this:
Either rendering the map first and use the resulting depth buffer when rendering the billboards
Or render both the map and billboards on the multi-sampled texture
Note that the above approaches are both meant to avoid having to distance-base sort a large number of billboards - but this remains a valid option and I have read about storing billboard locations in a quad tree for quick access.