Hello Rookhawk and welcome to the best forum,
As others have said here, the rifles and calibers you mention will likely do well.
Personally I know nothing about Accubond bullets though.
However, I do know a little about the .300 H&H, having used it in Alaska and Africa both.
IMO, there never has been a real burning need for all the other .30 magnums that followed.
(There certainly has been a burning market for them though).
The H&H version was designed for hunting thin skinned African game, especially for longer shots in open country.
And in open geography/sparse foliage, it is one of the very best for that use, which money can buy.
On my first African hunting trip, (Namibia/open hilly desert, cross canyon shots, etc.) I brought a .300 H&H and 180 grain Nosler Partitions at just a little over 2800 fps.
It worked so well that I would merrily do so again.
However, there were no eland or giraffe where I was and if there had been, I would have probably selected larger than .30 for that cause (not that giraffe interest me much anyway but, eland always will interest me).
As for the 7x57, it is a fine cartridge by reputation and like anything else, if you use the right type of bullet for the animals hunted and put it into their vitals, they will tip over/all will be well.
Again, I know nothing about the Accubond bullet but, despite today's - "haven't shot that many animals but I somehow know everything about it Technogeeks" - weeping over the NP bullet not being any good, regardless it is still an excellent bullet for African so called PG - in my opinion.
All the PH's I have spoken with on this agree for PG hunting but, some do not care for it on buffalo (lion yes/buffalo no).
For my Safari dollar, if I just had to bring the two rifles you mentioned, (I only like to bring one rifle per safari) I might consider working on an accurate load in the 7x57 with the 160 grain Nosler Partition or 160 gr Swift A-Frame, but that's just me.
I have never used the 7x57 in Africa but many do and seem very happy with it and I would not hesitate to use it if not hunting the largest PG species.
On that note, I would only bring the .300 / 180 grain and call it good.
As for "solids", I always bring a few that I have zeroed to the same point of impact as my softs but really only have needed one so far on a total of 4 safaris (had to shoot the buffalo shown in my avatar twice, one soft and one solid).
Some PHs suggest where legal, to bring a few (5 or 6 will do) solids for the miniature antelopes like duiker, klipspringer, steenbok and such but, I have shot these with softs and not splattered them too badly (I do not shoot any ultra high velocity cartridges when hunting in Africa).
Last but not least, my friend Lee DeSmet from Minnesota brought a .300 H&H on his first safari and used with great affect, 220 grain Hornady round nose softs (not sure what velocity) in the Limpopo District of South Africa (relatively thick thorn forest).
I was there and he returned to camp several times, with some very fine animals, large and small, plus a huge grin to match, rather supporting the notion that the old .300 H&H is still a fine "plains game" cartridge.
Sorry for the length of this rant but, I had too much espresso this morning (pretty feeble excuse - I just talk too much).
Blah, blah, blah, out.
Velo Dog.