Hello again, guys!
I'm in a hurry to share the news about resolution of the issue I described earlier.
I opened a ticket at Bittrex 2 days ago. After a short period of time I received a message with further steps on how to make your funds credited to your account. Those steps concerned depo wallet, transaction IDs, and still the main thing: the depo message which is attached to an address. I gave the credentials and has been warned that the crypto-funds in this case would be manually deposited by them (bittrex support team). Also, it was clearly said that this process actually takes approximately one week to be accomplished. For me, it took 2 business days and I received email that depo was credited. So it depends on unknown circumstances.
Now everything is fine, hope it helps those who stuck in this situation.