After n-th attempt to full resync with fresh setup it stuck again at "blocks":337902. "version":"v1.6.0.2-g" Log is full of "Orphan block" messages.
Why we full resync? - because it forks all the time.

Thank you Velvet78 for posting archived data folder link. It helped to get wallet to block 598476 by this moment. We still see "Orphan block" in log and it syncs extremely slow - about one block per 2 minutes while having 11 active connections. It much slower than a speed of new block creation which is 1-4 blocks per minute. Our server is fast and connection is good. Other wallets works flawless on it.

It's definitely something wrong with network/wallet. We will look how it syncs for a couple of days and if it turned to be impossible to sync it and dev will not take any action to fix it - we will have no other options but to consider coin is broken and remove 1337 from exchange without any possibility for withdrawals.