A way to express LTL (varient) to enforce a stream of data to satisfy some linear time logic
This is an interesting question.
It is not directly an LTL (Linear Temporal Logic) question -- rather a question about whether there is an algorithm or tool that takes an input stream and modifies it a somewhat minimal way to satisfy a given LTL property.
Whether that you want can be done or has been done depends on what exactly the allowed modifications to the stream are. In your example, you are, in a sense, remixing two streams. Note that LTL is defined over alphabets in which every character can have multiple propositions that are TRUE at the time. So in your example, you could have just mixed the u and v stream together to obtain:
u,u,u,u,{u,v},{u,v},....

This would have satisfied the LTL formula as well. If the way in which you remix is that the proposition in the output stream is always a subset of the propositions set in the input stream, then you can use reactive synthesis to obtain a transducer that does the stream mixing/fixing. However, this will only work if for every output stream there actually is a way to perform the mix.
If there is some quantitative notion of mixing/fixing, then quantitative synthesis may be a research area that may have some results. But you would need a description of the precise stream modification optimization criterion to see if any of the results from that area are applicable.