Firing Phasers At Warp.

[Kamen Rider Blade]

Transporters supposedly had nothing to do with Subspace, since the buzzword was never used in the context - until it was, when establishing that Subspace Transporters are a separate thing altogether ("Bloodlines", "Raijin"), but not before first establishing that there was a Subspace Frequency involved in the regular system ("Best of Both Worlds", "Data's Day").

That's two mentions essentially against and two for. But one is all it takes, in this fake reality, and the things said in "BoBW" and "Data's Day" make it quite clear that subspace is involved there, while the other two merely give a fancy name to a speculative technology without establishing much about working principles. Perhaps phasers thus also involve Tachyons - and we simply haven't gotten our single mention of this yet?

I would suspect that the "Data" portion of your Molecular Pattern Arrangement is sent via SubSpace radio. It's much Faster, higher bandwidth than over Normal Space radio, less things to interfere with it. That being said, Memory Alpha states that normal Transporter use for the Matter Stream is done over "Regular Space".

SubSpace Transporter with sending the "Matter Stream" via SubSpace is a separate type of Transporter.

One that has FAR more range than normal Transporters.

As far as Tachyons being part of "Phasers", I'd say the writers are reserving it for when they need to deal with Time Traveling shenanigans.