Call Me at This Number

Question

Come play with me in chat if you know my word!

Across
1. Mil. survey  
6. French act?  
10. System that the FIFA World Ranking is based off of  
13. Tool for Messner  
14. This and that  
15. Pinisi part  
16. Phase preceding ovulation  
18. Titular Salinger girl  
19. Abstract thing  
20. Raised  
22. Teacher's favorite student   
23. Easter Island figures  
24. Agreed (to)  
28. Stupor  
32. 2013 Katy Perry single  
33. Cinderella teams, perhaps  
36. MRI tech.  
37. 📞 x2  
39. ___ de deux  
40. Weaken or soften  
42. Equivalent  
43. British political party  
44. Recycles paper  
47. "Are not!" retort  
50. One of four major North American sports leagues  
51. Morning stimulant  
54. "Ain't Misbehavin'" director Richard  
58. Disturb a pond perhaps  
59. 📞 x5  
61. Ticked off  
62. It's fed by the Huron  
63. Ammonia-derived compound (var.)  
64. 📞 +1  
65. Nine-digit nos.  
66. Hinder  

Down  
1. Teeming (with)  
2. MBA subj.  
3. Sixer or Knick rival  
4. 📞 -8  
5. Stepped out of the room  
6. ___ Dhabi, UAE  
7. 📞 -1  
8. "Invisible Cities" author Calvino  
9. Put in jeopardy  
10. Steinbeck novel "___ of Eden"  
11. 📞 ÷3  
12. Samsung TV material  
15. Early NASA oceanographic satellite  
17. Cell (suff.)  
21. Quality of a leader, to Machiavelli  
24. "Journey" lead singer Pineda  
25. CSV part  
26. 📞 +2  
27. Spinal membrane  
29. Mt. Everest locale  
30. 📞 +4  
31. Plural indicators  
34. Sgt.'s subordinate  
35. Diviner  
37. D'Artagnan's hat accessory  
38. TV Guide listings  
41. Procrastinated at work  
42. ___ Text, code editor  
45 "La La Land" actress Stone  
46. 📞 +1  
48. They're unique  
49. Pigment found in purple grapes  
51. Home, slangly  
52. Like a light cake  
53. Leave after a bank heist  
55. "Get ___!"  
56. Resort town in Cornwall  
57. River that was the site of a WWI battle  
60. ___ Moines, Iowa  

Answer is a word.

Answer 1

The filled grid:

The aha moment:

Several of the clues have just a phone emoji, along with an arithmetic operation. The flavortext for the puzzle hints what to do: "Come play with me in chat if you know my word!" is a hint to the game of Contact, a word-guessing game occasionally played in a particular chatroom here on Puzzling.

The next step:

Each of these words was the "defender"'s secret word in at least one game of Contact: BYE, CALIPER, CAROB, CRAMP, GOLEM, LIME, MENDACIOUS, PARVENU, PLACID.

The clues that try to guess the secret word are numbered. Applying the operations to the numbers of the winning clues gives a number between 1 and the length of the word, each time.

Using that number as an index into the word, then sorting the resulting letters in chronological order by game played, gives the answer: PRESERVED.