ST Hyperspace Technology/Tracking in TLJ

So instead of using a new method that hadn't been seen in the movies before (but was hinted at in Rogue One), it would have been "much better" to use another new method that had never been seen in the movies before, for what reason exactly?

Sounds more like you are complaining for the sake of complaining. This method served a purpose, and it set up a part of the plot that the methods you mention couldn't have. Whether you liked that part of the plot is irrelevant, what matters is that this specific method allowed it to happen, while your ideas wouldn't have.

 

It just feels pointless.
Rather than Finn sent to switch off something easily remedied how about they infiltrate the Supremacy to delete the records the Republic has on Leia's Resistance thereby once deleted the Resistance can jump clear as their pursuers no longer have access to those ships transmitters long enough for them to get clean away?

 

So instead of using a minor detail that only exists to explain part of where the plot moves, you want to have a slightly different minor detail that accomplishes the same but in a much worse construed fashion. How is that supposed to make sense?

Why would the records about the resistance matter in any way?
And why would the Supremacy be the only ship in the entire FIrst Order fleet that has these records?

 

Now what if that map to Luke was actually Leia's way to discover how badly Snoke had infiltrated the New Republic.
Rather than introducing something that wouldn't be restricted to just one ship, you instead reveal the Republic's distrust of Leia by tagging all the ships they supplied her so Snoke's spies supplied those transmitter frequencies using them to stay one step ahead of the Resistance thus supporting the New Republic's stance on not doing anything about the First Order!
Once Hosnian Prime was blown up it meant accessing the heart of the Supremacy allowed them to delete those records in a way that filters throughout the First Order Fleet that appears to not make use of a homeworld so by the time anyone realised what they had done most of of all records on Leia's Resistance and quite probably the original Rebel Alliance deleted beyond recovery thus explaining how they could regroup effectively enough by Episode 9!