We present updated calculations of stellar evolutionary sequences and detailed nucleosynthesis predictions for the brightest asymptotic giant branch (AGB) stars in the Galaxy with masses between 5M(circle dot) and 9M(circle dot), with an initial metallicity of Z = 0.02 ([Fe/H] = 0.14). In our previous studies we used the Vassiliadis Wood mass-loss rate, which stays low until the pulsation period reaches 500 days after which point a superwind begins. Vassiliadis Wood noted that for stars over 2.5 M-circle dot the superwind should be delayed until P approximate to 750 days at 5M(circle dot). We calculate evolutionary sequences where we delay the onset of the superwind to pulsation periods of P approximate to 700-800 days in models of M = 5, 6, and 7 M-circle dot. Post-processing nucleosynthesis calculations show that the 6 and 7 M-circle dot models produce the most Rb, with [Rb/Fe] approximate to 1 dex, close to the average of most of the Galactic Rb-rich stars ([Rb/Fe] approximate to 1.4 +/- 0.8 dex). Changing the rate of the Ne-22 + alpha reactions results in variations of [Rb/Fe] as large as 0.5 dex in models with a delayed superwind. The largest enrichment in heavy elements is found for models that adopt the NACRE rate of the Ne-22(alpha, n)Mg-25 reaction. Using this rate allows us to best match the composition of most of the Rb-rich stars. A synthetic evolution algorithm is then used to remove the remaining envelope resulting in final [Rb/Fe] of approximate to 1.4 dex although with C/O ratios > 1. We conclude that delaying the superwind may account for the large Rb overabundances observed in the brightest metal-rich AGB stars.