Ahh, so it's not actually a new drive either, right.
The fact that you're pulling your data over the network is going to limit your max speed to less that the drive can do since the most you can pull is about 112MB/s and the drive will do 160MB/s even if you do have multiple 1Gb network connections at both ends, it's still a single stream, but as you aren't even getting close to that it's unlikely to be the problem.
If you haven't already it might be worth running a cleaning tape through the drive, and if that doesn't help try some different block sizes perhaps. My repo and drives are on the same machine so I don't have to worry about network bandwidth or latency from a shared storage system. The only other thing I can think it might be is that data matching speeds for LTO6 are higher than LTO5 and if you can't feed the drive above it's minimum data matching speed it'll have to rewind and slow things down massively. If that were the case thoguh I wouldn't really have expected the drive to be able to max out the LTO5 data rate that it was obviously doing.
I believe Veeam support has a tape drive testing tool that can confirm the drive itself can push it's full data rate. That might be the next step.