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 5 M &sun; and 9 M &sun;, 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 &sun; the superwind should be delayed until P ≈ 750 days at 5 M &sun;. We calculate evolutionary sequences where we delay the onset of the superwind to pulsation periods of P ≈ 700-800 days in models of M = 5, 6, and 7 M &sun;. Post-processing nucleosynthesis calculations show that the 6 and 7 M &sun; models produce the most Rb, with [Rb/Fe] ≈1 dex, close to the average of most of the Galactic Rb-rich stars ([Rb/Fe] ≈1.4 ± 0.8 dex). Changing the rate of the 22Ne +α 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 22Ne(α, n)25Mg 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 ≈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.