Of course early Christians thought Jesus was God, as evidenced by the dozens of quotes on this thread.
Your own quote above from Polycarp is naming Jesus as "God" :
may He bestow on you a lot and portion among His saints, and on us with you, and on all that are under heaven, who shall believe in our Lord and God Jesus Christ
Your post PROVES that the earliest congregation leaders viewed Jesus as both Almighty God and man .... at the same time, and not just one or the other.
And, as difficult as that may be to wrap your mind around, that is exactly what Christians believe today. I believe that your difficulty is rooted in materialism, which is the belief that there is no personhood attributed to anything other than the body of man - a leftover from Watchtower exposure.
Once you adopt a biblical definition of how man is constructed... with spirit, soul and body - a Tri-Partite being; then you will no longer need to ignore or explain away data that shows Jesus was viewed and accepted as God.
Read your last quote from Polycarp again, the whole thing. You'll see that Polycarp both acknowledged that Jesus had a God and was God. And, this is precisely the portrait that the scriptures present, regardless of how contradictory this may seem to someone with a partial materialist view.
It matters not if you agree, understand or accept this fact. This is the consistent portrait of Jesus of Nazareth, and is foundational to the Christian faith.
If you claim to be Christian, you have got to put faith in the right Jesus in order for the relationship to grow.