Ok, so it's not a 4003, but I have TI flats fitted to my 1980 4001 and it has the lowest action of any of my basses.
No buzz anywhere unless I really dig in with a pick.
I've often read, that being so low-tension, TIs need a slightly higher action than many other strings and this makes sense.
Strangely this isn't the case with my Rick.
Keep playing with your setup.
You'll get there!
'80 Rick 4001. '84 Fender Power J Special, '05 USA Jazz, '11 USA Precision, M Miller Jazz. Peavey T-40, Zoom B3. GB ShuttleMax 12.0, GB Uber410, fEARful 212.