Top-voted answer here on stackexchange helped a lot. Now parity is downloading around 2-10 blocks per 5 seconds.
I used these arguments:
parity --mode active --tracing off --pruning fast --db-compaction ssd --cache-size 4096
I believe that you may change many parameters, but the changes will not apply retroactively. So, you may not change anything in genesis block. Also, if you set transition block number option, such as bombDefuseTransition, the block number must be in future, and if you change/remove transition block number option, then both, current and new block numbers ...
It is also possible with go-ethereum. Tested with a simulated blockchain backend.
run parity -lsync=trace
looking for: "IO Worker #3 TRACE sync Checking snapshot sync: X (peer: Y)"
Search for the largest number Y in (peer: Y)
then copy X
stop parity and remove -lsync=trace
open ".../.local/share/io.parity.ethereum/config.toml "
and update config.toml with warp_barrier = X
run : parity