May I respectfully ask if it is your wish to hunt these animals or simply collect them as specimins regardless of the methods used?

The reason I ask is this. Hunting is hunting. If you wish to go to a large property where these species are known to be either from put and take or that there is a sustainable population on the property that is resident. Then you could be there for a very long time if you wish only to shoot these specific species.
For instence Jaco (SAHunt) and I chased Eland for 7 days, a month ago, without a realistic possibility of a shot. I did get other species, none of which were great trophy heads, but we worked dammed hard for them and I enjoyed every moment of it.
Now there are plenty of outfits that I could have contacted and told them I wanted an Eland. It would have been released 24 hours before I got there and I would have been set up in a hide or off a vehicle to shoot it as it would have not strayed far from its release point. In that case they could not ony give you the pedigree but tell you what it had for breakfast.

What I am getting at I think is this. If you want a good trophy of any specific species, then you may not get a shot at it even if you are there for a month hunting every day. That is not to say however that you may not get a shot at some superb specimin of another species. Thus you risk coming away disapointed with your African hunting experience, or taking the other option and closing your mind to the means by which the trophys are obtained, which to me at least is equally unsatisfactory.
That is what Ann is alluding to I think.

As it is your first time. Unless you have unlimited time and money I would do what Ann suggests get a recomendation for a good outfit that has some of the species on you hit list as well as others. Book a couple of weeks. Go with a good mind, chill out and take what comes as it comes.

Best wishes