Tardis is good stuff and will likely remove most protection. Just top it up. Carlack goes a long way so you'll need to reuse very little. Also, putting it onto a contaminated car like that will just trap in dirt effectively.
I find that carlack takes the tar off no probs! Just takes a bit ov time I never polish/seal my car all in one go! I just do a few panels at a time, once finished I start again!! Labour of love I think they say its theroputic!! Whites a great colour, once its clean its clean and there's no need to go mad with wax, its only gonna shine so much! My last car was a black polo gti, I went mental with all different types of wax, collinite marque d' elegance(915) was my fav.