I am in exactly the same situation. Also have a sedan without a tow bar, and the strap on bike rack just irritates the hell out of me.
It scratches my car, takes too long to load the bicycle to prevent damage to the bike, plus once the bicycle is loaded, I cannot access my boot. (The last point is very irritating since I have 2 young girls who always need something from the boot...
Also noted that with the bicycle behind the sedan using the strap on rack, the fuel efficiency drops dramatically.
So my options are:
1. Buy towbar and rack with tilt function
2. Roof rack.