Doug It sounds like you have a big problem!
You need a good risk assessment done, The soloution will become evident
Here is how - (A) Spot the hazard - clearly identify the problem.
(B) Assess the risk - Obviously it is an intollerable one.
(C) Fix it
(D) Early A.S.A.P.
This is the "S.A.F.E." system.
Do this by Eliminating the problem,Substitution, Engineered controls, Signage, Provide personal protective equipment & train your operators and your pedestrians.
For a company to suffer the described occurances you must have the pedestrian and forklifts working in the same area at the same time, If you can not separate them then you must train them to co-exist through policy/ proceedures & training.
Human life is the most important thing to be conciderd here.
Ask yourself "Is your company placing unreal expectations onto your drivers (this could be unstated but real none the less).

Priority should be given to creating a 3 meter exclusion zone around each forklift ( a no go zone).
I tend to think that too much speed is also involved here and also.
Priority shoul also be given to ensureing management awareness of the situation,
because management is responsible for the situation & soloution.
You must act immediatly and do not be hesitant to call a spade - a spade - state it as it is & where it needs to be said.
Don't forget to go back and to write down the common factors in all your incidents, this will point to the root cause or causes (a combination of factors).
Good Luck.
Dangerous.