Well if your carrier is requiring you to send btn then you still have work to do. Character Y does work you simply need to adjust it to suit your specific needs.
I once created system SCs like
1DialedTenDigits,,YSixDigitPinNumber + STenDigitBTN
So if I were to make up numbers the full sequence is
S - Calling Number
Place any following digits into the outgoing call's calling number field.
• Outgoing CLI Warning
Changing the outgoing CLI for calls requires the line provider to support that function. You must consult with your line provider before attempting to change the outgoing CLI, failure to do so may result in loss of service. If changing the outgoing CLI is allowed, most line providers required that the outgoing CLI used matches a number valid for return calls on the same trunks. Use of any other number may cause calls to be dropped or the outgoing CLI to be replaced with a valid number.
• Changing the outgoing CLI on calls using SIP trunks is not supported.
• On mobile twinned calls, if the original party information is used or a specific calling party information CLI is set, that number overrides setting the outgoing CLI using short codes.
Maybe you need SI
i - National
Both the S and SS characters can be followed by an i, that is Si and SSi. Doing this sets the calling party number plan to ISDN and number type to National. This may be required for some network providers.