Perhaps EIA information is not the best, but the PUCT does compile rates offerings data by classifications of kWh usage from reportings from the Retail Electric Providers in the deregulated part of Texas (ERCOT) and the monopoly bundled service providers outside of ERCOT and those exempt from competition (El Paso Electric, Southwestern Power Electric Co, Xcel Energy-SPS and Entergy Texas, plus Coops and Munis).
The data goes all the way back year by year and month by month starting with the open of competition in the ERCOT control area of Texas. From the info provided, it is not difficult to figure out the price/kWh offerings. I haven't dug through all the info, but the RETAIL rates appear to be close in and outside of ERCOT. I say RETAIL because there are other inputs like Transmission and Generation charges that differ among grid control areas that complicate the calculations. For instance, transmission rates in ERCOT are set by the PUCT and those outside of ERCOT are set at the federal level by FERC. Generation outside of ERCOT is regulated by the PUCT but ERCOT generation is unregulated.
REPs in ERCOT info by investor owned T&D service area (Oncor, CenterPoint, AEP Texas, TNMP):
http://www.puc.texas.gov/industry/electric/rates/RESbill/RESbillarc.aspx
Investor owned utilities outside of ERCOT and Munis/Coops exempt from competition:
http://www.puc.texas.gov/industry/electric/rates/NCrate/viewdownarc.aspx