(1 Peter 2:3, 4) is not a quote from Psalms.
And they would not be using the septuagint.
"How can the Watchtower Society reconcile Isaiah 44:24 with Hebrews 1:10?"
What is there to reconcile?
Isaiah was addressing the Israelites and they have followed false gods. That is why vs 6 says "There is no God but me". Jesus is not God like him. As vs 7 says "Who is there like me? Let him call out and tell it and prove it to me! From the time I established the people of long ago,"
Here it is not a matter of Jehovah vs Jesus. It is Jehovah vs the gods of the nations. Context is so important.
If Paul quoted that in Heb 1:10, he wasn't referring to Jesus. In Heb 1 he starts out saying "Long ago God spoke to our forefathers by means of the prophets on many occasions and in many ways. Now at the end of these days he has spoken to us by means of a Son". So it is clear that Paul knows that God used people prophets and now a Son. So he recognizes Jehovah and Jesus.
Context is so important.