B787 Captain reported loss of one GPS and clock failure that led to requiring voice reports to report position. The reporter noted checklists and bulletins failed to offer guidance for the situation.

Narrative

When [I] came up from break; was informed that after exiting potential GPS jamming area with GPS's off; L GPS didn't come back. R GPS fine and ANP was .03. Advised Dispatch and concurred with them that with one good GPS and two Inertial Reference Systems (IRS's); we were good to continue to our oceanic crossing. Dispatch indicated he had seen this GPS issue before.After a while; the aircraft clocks insidiously failed. The FO's clock alternated between two different times that were 4 minutes and 30 seconds apart. The Captain's clock did not vary. That led us to believe the FO's clock was bad. We conferred multiple times with Dispatch on the possible time implications for position reports; etc. Then; we got an ATC message that said our downlink was a future time; we were also asked over the radio to confirm our RNP. We explained one GPS inoperative but had one good GPS and two IRS's and that ANP was .03. We compared the FMS ETA to our next point with ZZZZ Radar and confirmed the Captain's clock was actually fast by 4:30 and our ETAs off by the same. ANP still fine at .03. SATCOM call with Dispatch; who called ZZZZ1 for us to advise them. Dispatch reported that ZZZZ1 said we could continue; and surprisingly; that we were not the first to have this problem this morning - and that we should make voice reports. When we called via HF; we asked if we should disconnect CPDLC so they didn't get erroneous position reports; but they asked us to stay connected for any other messages. We made voice position reports; adjusting for the time difference. At one point; the clocks came back for a short time. While it took a couple hours to work through all this; it was an uneventful crossing. ANP was usually .03 - the worst we saw was .04. As side note; we were told to contact ZZZZ2 on VHF crossing ZZZ. We put that in the reminders page and monitored our ALT NAV page. To our surprise; the reminder page went off saying we crossed ZZZ; yet our ALT NAV page said different. ZZZZ2 indicated they had a note that we may have GPS problems; we explained that we believed our navigation was fine (ANP still .04) but our clocks were off. She confirmed our clock error and said nothing about any navigation issue.While the bulletin on GPS jamming gives some good guidance; there is no guidance in case you have only one GPS - let alone if the clocks go off. NAV SINGLE GPS does not have any checklist associated with it. Flight Manual (FM) doesn't really help either. The GPS interference checklist is not really helpful. It says that the system should operate correctly even if only one GPS has recovered." Not in our case for the clocks."