The brute-force nature of periodograms also makes the algorithms readily available to parallelization. The NASA Exoplanet Archive has optimized its algorithms to be fully parallelized across a 128-core cluster. If we do not get a server/workstation set up, we may want to consider submitting our jobs to this platform. Computation times can be reduced to less than a minute for time-series data with hundreds of thousands of data values. 
https://exoplanetarchive.ipac.caltech.edu/cgi-bin/Pgram/nph-pgram