I worked up a little program to test the idea of using a string array to mimic writing to the screen. Seems to work OK.
10 REM SIMULATED LOCATE USING AN ARRAY
11 REM USING RAND DEF TO RANDOMLY PLACE CHARACTERS ON THE SCREEN
12 RANDOMIZE
13 DEF FN RN(S, L, H) = INT((H - L + 1) * RND(S) + L)
14 REM SET UP STRING ARRAY TO MIMIC SCREEN ROW, COLUMN ARE 0 BASED 24 LINES SO LAST LINE CAN BE USED FOR INPUT
15 DIM SCREEN$(24, 80)
16 REM RESET ARRAY AND PRINT TO CLEAR SCREEN
17 GOSUB 640
18 GOSUB 550
19 INPUT A$
20 FOR I = 1 TO 20
25 ROW = FN RN(1, 0, 23)
30 COL = FN RN(1, 0, 79)
40 SCREEN$(ROW, COL) = "*"
45 NEXT
46 REM PRINT TO SCREEN
50 GOSUB 550
51 INPUT A$
55 REM CLEAR SCREEN ARRAY
60 GOSUB 640
65 REM PRINT BLANK SCREEN
70 GOSUB 550
71 INPUT A$
80 END
545 REM PRINTS ARRAY TO SCREEN
550 FOR II = 0 TO 23
570 FOR JJ = 0 TO 79
580 PRINT SCREEN$(II, JJ);
590 NEXT JJ
610 NEXT II
620 RETURN
630 REM RESETS SCREEN ARRAY
640 FOR II = 0 TO 23
650 FOR JJ = 0 TO 79
660 SCREEN$(II, JJ) = " "
670 NEXT JJ
680 NEXT II
690 RETURN