The biggest issue is the imbalance in stresses within the log. When the log is still a part of a growing tree, those stresses are held in equilibrium, but as soon as the tree dies and moisture stars to evaporate, its cell structure shrinks a little and stresses move into imbalance.
Consider the growth rings....a growth ring close to the pith may be only a couple of centimeters in perimeter, so 10% shrinkage while it dries could result in a couple of millimeters of shrinkage. However a growth ring close to the bark of a 13" diameter log, is about 100cm, so shrinkage could be as high as 10cm. In reality that's going to result in one or more cracks running down the length of the log, and there's not a lot that you can do about it.
Slowing down the rate of moisture loss helps the stresses to be relieved more slowly, and thus causes less cracking, but does not eliminate cracking. Coating the ends of the log will achieve that, but there is no guarantee (in fact, it's unlikely) that a log this size will not crack. The ancient wisdom in this matter tells us that air drying wood takes about one year per inch of thickness - in our climate - but that's a long time to wait to discover the cracks in your log!
As Steve says, getting it hollowed as soon as possible is one solution. By removing much of the excess timber, the drying process will be much quicker and there will be less imbalance left in the log for its internal stresses to cause the cracks.
There is, however, one important issue that has not been mentioned.....the African Djembe is a traditional design native to West Africa, where the cell structure of the trees is different to that of English beech, and where the climate is very different to ours. That's why bongo and djembe makers in UK tend to start with flat planks and make up the drum bodies out of segments. I'm not saying that making a djembe in the traditional way is not going to be possible, and I applaud you for having a go, but it's going to need a skill-set and knowledge-base that you may not yet have considered.
I wish you well in your venture....Les