I have been interested following this as I think that the confusion you felt is probably quite widespread. However, In my experience of flying through class D the phraseology upon entering the zone has usually been something to the effect of:
Approaching the zone - G-xxxx, cleared to enter controlled airspace, VFR, not above altitude XXXX' Route present position towards xxxx,
if passing overhead Report the airfield in sight (for tower freq changeover).
Then on reaching the zone boundary - G-xxxx radar control service.
This is not precise but close as I recall, the main point being that its a VFR clearance, with a not above altitude xxxx, and without any instructions to 'steer heading xxx'. I have always assumed minor deviations in heading, whether to avoid another aircraft or even overflying a ground feature, are not prohibited, and ultimately as you are under radar control and therefore observation you will probably be prompted if any change in your heading is seen as unacceptable.... also being a 'not above' clearance would imply to me that there is probably a CTA overhead busy with hold traffic etc and that the grant of permission would probably be awkward to the controllers, but nothing wrong with descending to maintain a suitable separation is there if necessary?
As we know there is no separation provided in Class D between VFR and VFR flights so gotta do what we gotta do within the bound of our clearance to maintain our own, equally there is no separation between VFR and IFR for that matter, just 'essential traffic' info if my air law knowledge serves memory correctly
I would be interested to hear if any of this is incorrect to avoid making any embarrasing slip-up's down the line, but this has not got me in any bother yet
