Normal verticutting won't achieve what you are looking for. Aerify as deep as possible with the largest tine possible and as often as possible. You might even want to consider double aerifying once or twice. Basically, go through the normal process of aerifying the greens, topdress, then aerify and topdress again the same day.
A USGA article from Todd Lowe states the process:
"An innovative technique to improve putting green playability without sacrificing turf health is to double-core aerate. Double aeration includes coring the greens, removing plugs, backfilling holes with sand, and then performing this same operation in a slightly different direction the next day. Large diameter tines (3/4-inch) are often used with this operation to increase sand incorporation into the rootzone and to dilute organic matter. When large tines are used, putting greens generally require only two double corings each summer.
Double aeration can significantly reduce the number of closings for core aeration. Courses that normally close three or more times each summer can reduce to twice each summer with double aeration when large tines are used. Also, it allows the golf course to be open throughout most of May, a time when many courses allow reciprocal play.
The downside to double aeration is that it just takes more time (10 to 14 days) to recover. Many golf course superintendents take advantage of the closure by performing other necessary practices like cultivation (verticutting, scalping, aeration) of tees, fairways and roughs, or additional projects like tree pruning and drainage/irrigation improvements in the absence of golfers. Summer months are slow for most Florida golf courses, and closure is more acceptable at this time of year, especially when it improves playability and reduces the number of aerations."
Full text can be read here:
http://www.usga.org/course_care/regional_updates/regional_reports/florida/The-One-Two-Punch-For-Putting-Greens---May-2011/