We report on results obtained with the NEXT-DEMO prototype of the NEXT-100 high-pressure xenon gas time projection chamber (TPC), exposed to an alpha decay calibration source. Compared to our previous measurements with alpha particles, an upgraded detector and improved analysis techniques have been used. We measure event-by-event correlated fluctuations between ionization and scintillation due to electron-ion recombination in the gas, with correlation coeffcients between -0.80 and -0.56 depending on the drift field conditions. By combining the two signals, we obtain a 2.8 % FWHM energy resolution for 5.49 MeV alpha particles and a measurement of the optical gain of the electroluminescent TPC. The improved energy resolution also allows us to measure the specific activity of the radon in the gas due to natural impurities. Finally, we measure the average ratio of excited to ionized atoms produced in the xenon gas by alpha particles to be $0.561\pm 0.045$, translating into an average energy to produce a primary scintillation photon of $W_{\rm ex}=(39.2\pm 3.2)$ eV.