Set your spindle carefully in another lathe and make sure it turns true on external diameter close to chuck, in the middle and far away.
If you succeed then spindle is true. It is impossible to achieve it with a bent one.
Once done insert test bar into taper socket and check with DTI both ends of the test bar.
If the bar "wiggles" then your taper socket is surely misalligned. If it doesnt then you are not reasembling your spindle correctly.
Another approach is to install a chuck in your existing spindle mounted in the lathe.
Then grab test bar, eg 1 inch diameter linear bearing bar in the chuck and allign it true (make sure chuck grabs it straight). Make DTI readings on both ends of bar, close to chuck and close to far end.
If you get the same readings your spindle must be straight. Now insert test bar with tapered end into Morse socket of the spindle.
If wiggling increases with distance (towards end of test bar) *and* your initial test with test bar was OK then tapered socket is *definitely* misalligned and need correcting.
Martin