Then there will be other possibilities to get engines elsewhere as an interim solution, you act as if there are no more alternatives on the market.
The Shenyang WS-10 Block C or D, for example has FADEC (this is based on the CFM56 engine which is essentially the core of the F101/F-110 family) it comes quite close to the F-110 in terms of performance and durability parameters, or even slightly above it, while at the same time it is only slightly longer than the F-110, the weight and diameter are about the same.
The Chinese would probably even offer a technology transfer, and quickly deliver e.g. 80 engines.
Just to drive a wedge within NATO that they distrust Turkey, which they have always done, see the sanctions and embargoes in the past by the US & EU.
To be clear, the US & EU are not friends and never will be.
If they could and if the damage to themselves was not so great, they would have wanted to break up Turkey in several pieces long ago. Only the massive fear and absolute resistance keeps them from doing so.