Starfleet switches from phaser banks to arrays around 2322, when the Ambassador-Class is first produced. The TNG warp scale may come in then as well. The Tomed Incident was about 50 years prior to "The Neutral Zone" on TNG, so ~2310-15. LUG would suggest they were fighting the Taur'hai during this period.
There is a very good timeline for technical and political developments in the forthcoming TOS supplement for Spacedock by the esteemed Steve Long, but I don't have the testread version on me right now.
"That might have been the biggest mistake of my life..."
"It is unlikely. I predict there is scope for even greater mistakes in the future given your obvious talent for them."
Vila and Orac, Blake's Seven