Solved. In case anyone else needs this, I found an old script called "MouseClickPlus.au3" in another thread and was able to modify it to include two different coordinates, a starting coordinate and a final coordinate, and thus performing a drag. It does this through user32.dll calls. Here's what the modified script looks like:
#cs ----------------------------------------------------------------------------
AutoIt Version: 3.2.8.1
Author: someone
Script Function:
MouseClickPlus
#ce ----------------------------------------------------------------------------
Func _MouseClickPlus($Window, $Button="left", $X1=0, $Y1=0, $X2=0, $Y2=0, $Clicks=1)
Local $MK_LBUTTON = 0x0001
Local $WM_LBUTTONDOWN = 0x0201
Local $WM_LBUTTONUP = 0x0202
Local $MK_RBUTTON = 0x0002
Local $WM_RBUTTONDOWN = 0x0204
Local $WM_RBUTTONUP = 0x0205
Local $WM_MOUSEMOVE = 0x0200
Local $i = 0
Select
Case $Button = "left"
$Button = $MK_LBUTTON
$ButtonDown = $WM_LBUTTONDOWN
$ButtonUp = $WM_LBUTTONUP
Case $Button = "right"
$Button = $MK_RBUTTON
$ButtonDown = $WM_RBUTTONDOWN
$ButtonUp = $WM_RBUTTONUP
EndSelect
If $X1 = 0 OR $Y1 = 0 Then
$MouseCoord = MouseGetPos()
$X1 = $MouseCoord[0]
$Y1 = $MouseCoord[1]
EndIf
For $i = 1 to $Clicks
DllCall("user32.dll", "int", "SendMessage", _
"hwnd", WinGetHandle( $Window ), _
"int", $WM_MOUSEMOVE, _
"int", 0, _
"long", _MakeLong($X1, $Y1))
DllCall("user32.dll", "int", "SendMessage", _
"hwnd", WinGetHandle( $Window ), _
"int", $ButtonDown, _
"int", $Button, _
"long", _MakeLong($X1, $Y1))
DllCall("user32.dll", "int", "SendMessage", _
"hwnd", WinGetHandle( $Window ), _
"int", $WM_MOUSEMOVE, _
"int", 0, _
"long", _MakeLong($X2, $Y2))
DllCall("user32.dll", "int", "SendMessage", _
"hwnd", WinGetHandle( $Window ), _
"int", $ButtonUp, _
"int", $Button, _
"long", _MakeLong($X2, $Y2))
Next
EndFunc
Func _MakeLong($LoWord,$HiWord)
Return BitOR($HiWord * 0x10000, BitAND($LoWord, 0xFFFF))
EndFunc