Bradley Anderson and Don Mahaffey are right in suggesting you talk to your clubs superintendent.
Because of the huge number of factors involved, no one on here can actually answer what you are asking. Its like asking an online golf pro to fix your slice without them seeing your setup or swing.
Regarding the greenway program and how I understand it:
The methods the are promoting are nothing new or groundbreaking. They are advocating creation of an environment via pH, water and nutritional management in which poa will struggle to be competitive and the desirable grasses will dominate. This is not some radical new concept but is simply a getting back to basics approach in turf management. These methods have been around for a very long time. They will however have a huge impact for clubs which are overwatered and overfed (the current situation at most courses).
Steve:
Do you have any idea if any poa annua strains could've survived in the original linksland swards that apparently only had natural agrostis (bent) and festuca (fescue) since some say they were the only grasses that could survive in that highly acidic soil?
Be careful not to generalise about bentgrasses.
Agrostis is a genus not a species and cover wide range of species.
The bents that are found in the UK and on links courses are predominantly: Agrostis capillaris (Common Bent; Browntop) (= A. tenuis)
The bents grasses used in putting greens in the US and much of Australia are: Agrostis stolonifera (Creeping Bent) (= A. palustris)
The creeping bents include A series, G series SR varieties etc.
The browntop varieties can successfully exist in very low pH values (I have seen them in 4.2) and an ideal range of 4.5 - 5.5. The creeping bents however have an ideal range 5.5 - 6.5 which is very similar to that of poa.
Acid theory promotes the goal of a pH value that the desirable borwntop will still remain strong in while at the same time discouraging the poa. I struggle to see how this can also apply to creeping bent with its similar pH requirement to poa.