Writing LTO-3 tapes with a LTO-4 drive

The first thing i would suggest is to run a cleaning tape through it at least once - possibly twice it'd bet there is a decent amount of dust on the tape heads. Which would cause symptoms like what you are describing.

Also have you tried a different tape? There might be somethign wrong with the tape.

Are there any logs on the backup machine as far as scsi errors?

As an asdide, note that 100MB/min is far below the minimum speed for tape streaming with LTO 3, so you're probably losing a fair amount of capacity with the tape stopping and starting (ie you're probably getting better than 1.5:1 compression, but this is lost in gaps in the data on the tape). This will probably be rather worse with LTO 4, as I think the minimum speed has gone up.

Disk - Disk - Tape will help with the minimum speed problem, and will give you some capacity for free.

If you're not doing it, strongly consider some kind of scheduled defrag of the disks on the servers you're backing up. 1000 MB/min is not a great level of throughput for gig ethernet on reasonably modern hardware. I'd expect that on even 2 year old machines you should be able to get 1800MB/min (that's only reading from the server disk at 30MB/sec), so there's scope for improvement.

Edit: For LTO 3, you really want a 256KB block size for best performance.

WRT shoe shining, There's no time for the tape to rewind if the buffer runs empty briefly, so it'll leave a gap on the tape.