Po' Anna, the impovrished turf of golf greens, is so misunderstood.
I've never been to Oregon, an I don't know if you are on the wet side of the state in Willamette Valley, but in cool, wet climates, Poa annua out performs every other species in every way, including year round putting surface and budget economy.
If you want to encourage the transition, then there are steps to be taken.
True, water helps, but there is no need to over-water until the greens play like baskets of wet laundry. Simply install a weather station and computer controlled automatic system and water each day to account for evapo-transpitration rates. The greens will be firm enough, and the Poa will thrive.
There are over 300 identified subspecies/genotypes/varieties of Poa annua. Most are ugly, but a precious few make the most outstanding putting surfaces on earth. Unfortunately, the most desirable subspecies of Poa are generally the least prolific seed producers. Nevertheless, if there are any courses near you with Poa greens you admire, ask them if you can have some of their mower clippings during the spring, when the seedheads are abundant. Mix those up with topdressing on your greens. This is best to do right after you aerate. If their greens arent producing any seed head to speak of, then ask for some aerator plugs and plant those in a nursery where you can let the plants grow up higher to harvest the seed.
While transitioning, mow low. Keep it under an eigth inch all year (3 mm). the Poa competes better with other species at lower heights. Also, the golfers will appreciate the speed.
Presuming you want the greens to play well during the transition, don't overdo the fertilizer. Three pounds/year of nitrogen is plenty, but double that in potassium. Spoon feed, applying miniscule doses weekly via liquid applications with a sprayer. Phosphorous won't make any difference, outside of the textbooks.
Also for transitional playing quality, begin a program of the growth regulators Primo and Proxy in tandem. This is essential to maintain uniformity and consistency on the putting surface. When it's done correctly, 98% of the people who play the greens won't notice that you are 50% Poa and 50% bentgrass.
Yes, you will nedd to initiate a preventative fungicide ("the "F" word!) program. I've been on one for years, and still I have managed a happy and productive life with a loving family.
Of course, these are only my opinions, and I may be wrong.
(But I doubt it).