I guess the TSU3000 is so lame that it may be worth changing the JVC.irp file used by MakeHex.
You got it nearly right in copying the repeat part into the one time. But it might work better if you add the repeat part onto the one time rather than replace:
The JVC protocol has that extra burst on just the first frame. The JVC.irp file has the extra burst instead of the whole first frame, because that OUGHT to give the same result. The extra burst is so short you couldn't release the key fast enough that it would be released before the extra burst is done. If the key is still pressed at the end of the one-time part, the only correct behavior for the Pronto is to immediately start the repeat part. But the TSU3000 seems to throw some extra pauses where they don't belong and gets this wrong.
Your JVC device may need a long enough press that even the version I posted above won't do it.
Do I understand Peter's reply correctly? That means the promised firmware upgrade that will allow direct control of duration has already been released? If so then that would be a better way of dealing with this problem.