First eliminate the POV characters who only meet one character from the list:
1. Will only meets two named characters in his whole existence - one of these is Waymar
2. Cressen spends his entire time on Dragonstone & the only listed character who has even been to Dragonstone is the Lord himself - Stannis
3. Merrett appears in only 3 chapters - negotiations at the Twins, the Red Wedding & his execution. The only listed character present at any of these events is Walder Frey.
[Blackfish did not attend the RW and Thoros did not attend the execution]
4. Pate hangs around Oldtown meeting nobody of consequence before being killed by Jaqen H'qar in his guise as 'The Alchemist'
5. The only characters Aeron ever meets are Ironborn, most of these are also POVs except for Euron.
6. As of the end of ADWD Jon Connington has only encountered his 'son' Young Griff

There is one listed character who has met just one POV:
7. Drogo dies before meeting any POV's except for Dany

There are now some more POV characters who have only met one from the reduced list of characters:
8. Davos was given an assignment by Wyman Manderley at White Harbour 
9. Asha couldn't remember Jeyne Poole's name after the escape at Winterfell
10. Victarion took Moqorro on board with him for some reason
11. Melisandre bust out some of her magic to disguise Mance Rayder 
(Her and Gilly do a pretty good job of avoiding each other as far as I can tell. I have accepted Gilly as a correct answer for the sheer proximity of the two characters but not taken account of this in the solution)

One more run through the reduced list:
12. Varamyr is present when Ygritte returns to the Free Folk

Two of the POV characters have never left Dorne and have therefore only met the same two listed characters.
The orientation of these two does not matter.
13. Arianne recruits Darkstar for her coup and is the daughter of Doran
14. Areo guards Doran and confronts Darkstar

Two of the listed characters are stuck in Essos. Neither have met Tyrion (yet) thus they have only met the same two POVs
15. Quentyn is insulted by Daario and incinerated by Rhaegal 
16. Barristan is bold in the general vincinity of both Rhaegal and Daario 

17. Arys has implicitly met quite a few characters due to his time on the Kingsguard, but the only character left who he has explicitly spent time with is The Hound

These 17 must be assigned correctly. 
From this point on there are multiple solutions but it is easy to head down a dead end without thinking a few moves ahead. 
Grouping characters by location works well as a strategy!

At or beyond The Wall:
18. Jon Snow is creeped out by Craster
19. Chett fails to assassinate Mormont after Other intereference
20. Samwell raises his fat pink mast in Gilly's direction
[These 3 can be linked in any combination]

Under the jurisdicture of Winterfell:
21. Bran is reek'd by Ramsay and journeys with Jojen
22. Theon mostly ignores Jojen and wishes he had been mostly ignored by Ramsay

All sorts of shenangians with the characters who have visited the Eyrie:
23. Only Cat can satisfy Littlefinger
24. Bronn defend Tyrion to the death
25. Sansa watches Lysa learning to fly
[These 3 can also be linked in any combination]

Meanwhile, in the Riverlands:
26. Pod goes on a wild goose chase with his Ser, M'lady Brienne
27. Arya talks resurrection with Thoros
28. Jaime plays his hand against the Blackfish

Finally at King's Landing
29. Cersei and Olenna engage in some thorny verbal sparring
30. Ned discovers Gendry's origin story
31. Ser Pounce is completely adorable; Kevan is underwhelmed