Working by hand your options are limited.
I dont like T-cut because it is an old fashioned abrassive cutting compound/polish, in the past few years the game has moved on.
Newer products contain diminshing abbrasives which mean they start off with a heavy cut, but break down into a mild finishing polish leaving a great finish. T-cut however does not, it stays abrassive no matter how long you work it/use it for and will install fine marks removing bigger ones.
To be honest your best option is using something like Meguiars Scratch X to remove defects by hand (mulitple applications will be required). Followed up with something more mild like Autoglym Super Resin Polish.
You should always try a mild polish first to see how it cleans things up before cracking out anything more harsh.