That's redefining the problem—if you add a timeout, you are explicitly making the language not Turing complete any more.

The language still is, just not the environment in which it runs. Much like a language can be Turing-complete without having infinite tape/memory to run on.

When people say "Turing-complete" it's usually assumed that we are talking about computational models which could emulate Turing machines given infinite memory. But we don't have infinite memory.

Adding time limits radically changes things.

Then you get valid programs timing out when they would have compiled otherwise.

Even if it's technically valid it's not likely to be a useful program if it has an unhalting loop in its data type declarations and enforcement.

It doesn't have to loop forever, it could just take a few minutes to calculate. There are plenty of useful, real-world projects that take hours to compile (see: any large project in C++). To reject these programs due to an arbitrary timeout is a non-starter.