Since the issue of adjourning games so that the next round can be paired has come up, how about a poll. TDs: When was the last time you adjourned a game so you could pair the next round?
This is why I hate increment.
More recent for adjournments due to site issues rather than pairing pressure. If I was slower pairing or chose time controls too tight then it would be more common.
Before SD, I think the hardest task I had to do is figuring out adjournments and their resumptions.
One time I knew someone was sitting on a theoretical endgame win and they asked me when I would adjourn the game (so he could reference an endgame book before resumption) - he was trying to make me do it sooner than later. He had about 50 minutes to make 5 moves so he was fine sitting for 45 minutes as he was at the strategical fork in the road.
The first time (maybe the only time?) I was involved with my game being resumed – indeed my opponent sealed an impossible move. I would have to say it was pretty clear what was meant – bottom line is the TD (a NTD) ruled it a loss.
I had someone in a dead draw (but up 1 pawn!) refusing to accept the draw in a 60+30 game recently. After the adjournment they took the draw, but they made us adjourn it first.
I don’t think I would do a +30 unless there was a ton of time before next round. e.g. like a weekly single game 
I did do a +15 but I added that 135 moves automatic draw (i.e. no adjournments/position adjudication) We actually wound up starting the last round early
The rounds were 3.5 hours apart against a nominal 3 hour duration; this was the only game that had any issues finishing well in time.
I hate increment generally, much less +30, but some players swear by it.
I found that just setting an adjourned move envelope by the players often resulted in them coming to an agreement on a result.
Does FIDE even allow for adjourned games these days? I think the last several Olympiads and world championship cycles haven’t used them. Fischer, as I recall, was upset that Spassky resigned an adjourned position in their final game in 1972 rather than have to concede defeat face-to-face.
What’s an adjourned game?
Joking of course. I’m relatively new to chess, but haven’t even heard of any of my players saying they tried to adjourn a game in the last 30 years.
Yes, it’s in the Guidelines provided together with the Laws of Chess (not part of the Laws of Chess but strongly recommended).
Guidelines I. Adjourned Games
I.1 Adjournment procedure:
I.1.1 If a game is not finished at the end of the time prescribed for play, the arbiter shall require the player having the move to ‘seal’ that move. The player must write his/her move in unambiguous notation on a paper scoresheet, put his/her scoresheet and that of his/her opponent in an envelope, seal the envelope and only then stop the chessclock. Until he/she has stopped the chessclock the player retains the right to change his/her sealed move. If, after being told by the arbiter to seal his/her move, the player makes a move on the chessboard he/she must write that same move on his/her scoresheet as his/her sealed move.
I.1.2 A player having the move who adjourns the game before the end of the playing session shall be considered to have sealed at the nominal time for the end of the session, and his/her remaining time shall so be recorded.
I.2. The following shall be indicated upon the envelope:
I.2.1 the names of the players,
I.2.2 the position immediately before the sealed move,
I.2.3 the time used by each player,
I.2.4 the name of the player who has sealed the move,
I.2.5 the number of the sealed move,
I.2.6 the offer of a draw, if the proposal is current,
I.2.7 the date, time and venue of resumption of play.
I.3 The arbiter shall check the accuracy of the information on the envelope and is responsible for its safekeeping.
I.4 If a player proposes a draw after his/her opponent has sealed his/her move, the offer is valid until the opponent has accepted it or rejected it as in Article 9.1.
I.5 Before the game is to be resumed, the position immediately before the sealed move shall be set up on the chessboard, and the times used by each player when the game was adjourned shall be indicated on the clocks.
I.6 If prior to the resumption the game is agreed drawn, or if one of the players notifies the arbiter that he/she resigns, the game is concluded.
I.7 The envelope shall be opened only when the player who must reply to the sealed move is present.
I.8 Except in the cases mentioned in Articles 5, 5.2.2, 6.9 and 9.6, the game is lost by a player whose recording of his/her sealed move:
I.8.1 is ambiguous, or
I.8.2 is recorded in such a way that its true significance is impossible to establish, or
I.8.3 is illegal.
I.9 If, at the agreed resumption time:
I.9.1 the player having to reply to the sealed move is present, the envelope is opened, the sealed move is made on the chessboard and his/her clock is started,
I.9.2 the player having to reply to the sealed move is not present, his/her clock shall be started; on his/her arrival, he/she may pause his/her clock and summon the arbiter; the envelope is then opened and the sealed move is made on the chessboard; his/her clock is then restarted,
I.9.3 the player who sealed the move is not present, his/her opponent has the right to record his/her reply on the scoresheet, seal his/her scoresheet in a fresh envelope, pause his/her clock and start the absent player’s clock instead of making his/her reply in the normal manner; if so, the envelope shall be handed to the arbiter for safekeeping and opened on the absent player’s arrival.
I.10 Any player who arrives at the chessboard after the default time shall lose the game unless the arbiter decides otherwise. However, if the sealed move resulted in the conclusion of the game, that conclusion shall still apply.
I.11 If the regulations of an event specify that the default time is not zero, the following shall apply: If neither player is present initially, the player who has to reply to the sealed move shall lose all the time that elapses until he/she arrives, unless the regulations of an event specify or the arbiter decides otherwise.
I.12 Resuming an adjourned game:
I.12.1 If the envelope containing the sealed move is missing, the game shall continue from the adjourned position, with the clock times recorded at the time of adjournment. If the time used by each player cannot be re-established, the arbiter shall set the clocks. The player who sealed the move shall make the move he/she states he/she sealed on the chessboard.
I.12.2 If it is impossible to re-establish the position, the game shall be annulled and a new game shall be played.
I.13 If, upon resumption of the game, either player points out before making his/her first move that the time used has been incorrectly indicated on either clock, the error must be corrected. If the error is not then established the game shall continue without correction unless the arbiter decides otherwise.
I.14 The duration of each resumption session shall be controlled by the arbiter’s timepiece. The starting time shall be announced in advance.