Ok so I don't go for honeymoon but with my father and sister for a private circuit in september in Tanzania... And I had the same question as you: What lens to take.
For the gear comparison:
Sometime you may use a shorter lens but 95% of the keepers for wildlife look to be @ 300mm. Some forumers have very nice picture taken with a 300mm. Look in my thread were I discussed my choice:
https://www.pentaxforums.com/forums/10-pentax-slr-lens-discussion/315922-tamr...ya-safari.html Fantastic Mister Fox in particular showed really great pictures. Go to his flickr by click on links. It is impressive what he managed with the 55-300. I would add that the 60-250 is not fully 250mm except at infinite and the 55-300 is f/4.5 bellow 200mm. There no much difference in light gathering and the 60-250 lack reach meaning its sharpness advance is partially lost. There much more difference in price weight and size than capability to me.
I would add that if you are not a wildlife shooter expert - and you are likely not one if you don't own any lens to do it - the biggest differenc will come from training. You need to learn how to operate the camera at 300mm framing, How to do tracking, how to use the right AFC settings, the kind of isos/shutter speed/apperture that work best etc.
You'd want to have the lens long in advance go to zoo, train on whatever you can find in other places: ducks, safari zoos, moving people, why not cows, dogs whatever at 300mm framing in your home location. The best would be to train month before without hurry on several session, have time to post process the picture, analyse, understand and let your brain process things in the background. That remove the renting option because you would need to rent the think at least 2 months then.
A trained photographer will do 10 time better on a 55-300 or something even more pedestrian that you with a 200-400 f/2.8 and a 1Dx. The photographer is ALWAYS more important than the gear.
For your honeymoon.
Man this is your honeymoon. You should spend your time in the bed doing other things than taking photos, the trip being only a side dish to accumulate great memory in a fantastic place.
If you both like the idea of safari, looking for wildlife (and I hope it if you decided for a safari...), your priority should be you both enjoy the experience. You need binoculars, ensure you don't get a cramped coach with one or both not seeing anything (usually the wildlife in only on 1 side of the vehicule). And each should have either the binocular or the camera in hand to be able to enjoy the experience fully.
If only you enjoy photography, be sure you don't do too much. Reserve lot of time enjoying the experience with your wife. It should be shared memory, a common experience not the other guys spending his day being the camera.
In the end I think at this time life you likely have many many things to buy and do. There no reason if you are not extremely wealthy to spend to much on side things like photographic gear. You'd want a house/flat, you'd need to buy everything inside, you'd want both a new car, you'd have a baby or 2... Yeah you think of renting, but i don't think that the best proposition. You need to train before, remember.