My opinion: Solo both portals at the same time. Maybe send an extra in for a few seconds to fire off a few rockets then leave if the two soloers aren't 100% competent at soloing. This is easily the quickest most efficient method IMO.
These are the 3 main strategies ive seen used with only mild variations, so if you use a method similar to one of the above vote for that one.
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I prefer doing both at the same time. But I often find myself being the only one that is capable of doing this. So I end up soling the first portal, come out and cleanse, drop the relic for someone else to pick up(pre-planned) then we both go in next portal