There is no way to change the behavior ReadLine, it will recognize CRLF only as a line terminator. Therefore, the only simple solution is the one you have already described.
Edit
In fact, there is another library that should be available out of the box on the ASP server, which may offer some help. This is the ADODB library.
ADODB.Stream LineSeparator, 10 13 CRLF , . , , ReadText. ReadText , -2.
: -
Dim sLine
Dim oStreamIn : Set oStreamIn = CreateObject("ADODB.Stream")
oStreamIn.Type = 2 ''
oStreamIn.Open
oStreamIn.CharSet = "Windows-1252"
oStreamIn.LoadFromFile "C:\temp\test.txt"
oStreamIn.LineSeparator = 10 ''
Do Until oStreamIn.EOS
sLine = oStreamIn.ReadText(-2)
''
Loop
oStreamIn.Close
, CharSet unicode, CharSet, , Unicode. "Unicode" , , UTF-16. , ADODB Stream UTF-8 Scripting.
, , MAC CR ? Unix, LF, ?