There will always be latency. Every recording you make will have latency.
If you use a Mac computer, you are already on the right track because these computers are generally used most for recording.
Choose a fast AD interface and you are good.
I have been using a Mac computer for years, with the advantage that you are not constantly reminded to update this or that driver, as with Windows.
Just because there happens to be a scoring mode in Logic doesn't mean you should use it. Logic has been one of the better DAWs in the computer world for years.
I use Logic and Reason on my Mac for all recordings.
Use a DAW written for Mac.
Not a port of a Windows DAW.
A good AD converter has one or more USB ports.
Connect the USB cable to the USB port of the T4.
When recording in the T4, turn off all effects and use the Logic effects to reduce latency a bit.
dE.niz