We present the first near-IR spectroscopy and joint analyses of multiwavelength observations for SDSS J082747.14+425241.1, a dust-reddened, weak broad emission-line quasar (WLQ) undergoing a remarkable broad-absorption line (BAL) transformation. The systemic redshift is more precisely measured to be z = 2.070 +/- 0.001 using H beta compared to z = 2.040 +/- 0.003 using Mg ii from the literature, signifying an extreme Mg ii blueshift of 2140 +/- 530 km s(-1) relative to H beta. Using the H beta-based single-epoch scaling relation with a systematic uncertainty of 0.3 dex, its black hole (BH) mass and Eddington ratio are estimated to be M (BH) similar to 6.1 x 10(8) M (circle dot) and lambda (Edd) similar to 0.71, indicative of being in a rapidly accreting phase. Our investigations confirm the WLQ nature and the LoBAL -> HiBAL transformation, along with a factor of 2 increase in the Mg ii+Fe ii emission strength and a decrease of 0.1 in E(B - V) over two decades. The kinetic power of this LoBAL wind at R similar to 15 pc from its BH is estimated to be similar to 43% of the Eddington luminosity, sufficient for quasar feedback upon its host galaxy albeit with an order-of-magnitude uncertainty. This quasar provides a clear example of the long-sought scenario where LoBAL quasars are surrounded by dust cocoons, and wide-angle nuclear winds play a key role in the transition of red quasars evolving into the commonly seen blue quasars.