[Rumil]

Welcome to the Barrow, Not Yet Dead!

thorny question indeed, unfortunately I don't think Tolkien mentions the Misty/Grey Mountains orcs much during LoTR, so its up to us to discuss possibilities.

I'd agree that, although they had lost heavily during the Battle of the Five Armies, their numbers could have recovered somewhat (but still be significantly fewer than if the battle had not occurred, and their expansion continued).

The only times we get to see Misty Mountains orcs in LoTR are in Moria and the combined Sauron/Saruman company that kill Boromir and kidnap Merry and Pippin. These included a group from the Misty Mountains that disliked the sun. So maybe Misty Mts goblins were sent to reinforce other armies, including Dol Guldur and Moria (that was seriously depleted in orcs according to JRRT), and maybe even Mordor? Perhaps joining up with Saruman might have seemed an attractive alternative for the goblins?

On the other hand, very little was writen on the Battle under the Trees or the Siege of Erebor, so we don't know if Misty Mts types joined with Dol Guldur troops in their attack on Thranduil, or even if some joined the Easterlings at Dale and Erebor. I'd guess that they did, but that's just a hunch.

The Beornings and Woodmen must come into this as well, prior to LoTR they kept the High Pass open and clear of goblin interference (perhaps slowing the re-population of the goblins). They are mentioned as fighting in Mirkwood iirc. Were they pushed back from the mountains by a goblin assault perhaps?

A very speculative proposal is that they raided West of the mountains. Only 30 Rangers could be summoned to help Aragorn, and the Shire was left unguarded. Many assume that there were many more Rangers - perhaps they (with Elrond's help?) were busy dealing with goblin and wolf incursions??

I do rather like your idea of orcish civil war and in-fighting reducing their numbers further after the Battle of the Five Armies. Since there were leadership vacancies I doubt that the succession process would be a bloodless one!