I've had a look at the program you're referring too, which is Plotting a series of points, apart from INK 0, INKs 1-15 are being used to simulate the movement of the snow, which is the most effective effect in Interpreted BASIC. Lines 1550-1620 simulate the movement through the rotation of the INK palette. To make the program 464 Compatible replace the FRAME in 1600 with CALL &BD19, though IMO Frame Flyback isn't necessary when Rotating the INK palette, in this program though it's probably slowing the effect.
You can use the Firmware to select where the screen is, but I don't think the Firmware allows you to draw to the other screen while you're viewing the other, @HAL6128 posted a Bouncing Ball demo in the Hisoft Pascal 4t thread which demonstrated the use of OUT to draw the next ball position while displaying the previous ball position onscreen. Though there were complications when getting that small program to run on a 464 & 6128. Were you trying to utilise 2 Screens to have no delay?
If the Text your writing to screen is in a single colour you could reserve one of the INKs for your text, which will still give you 14 INKs to play with. If you wanted INK 15 for your text (I forgot to mention the Animator program begins in MODE 1, but uses MODE 0 for the effects), you could change line 630 to:
630 c%=int(rnd*14)+1
510 should read:
510 if c%=15 then c%=1
those other lines need changing as well:
1570 INK (a% MOD 14)+1,0
1590 INK (a% MOD 14)+1,c%