How do you budget reconcile for a non-existent program?
That seems more like outright lies than anything else.
Explain more please ...
You're apply logic to a political process. Mistake number one.
So long as the President doesn't sign the Reconciliation Bill first, they (the Congress, to include both Houses) can pass legislation in whatever order they choose. While it's not frequently talked about, it's within the Speaker's authority to hold bills before being sent to the WH for signature. The only time such maneuvers are attempted, is usually when the majority is engaging in some Parliamentary shenanigans.