Attrition is a huge problem with exploration fleets at the start of the game. As technology levels increase, attrittion becomes less and less of a problem. Much later in the game, most fleets will become immune to any attrition in high sea. That's something to look forward to.
Here is a suggestion. As you explore Africa or any large land mass, make one or two coastal colonies along the way. Even a level one colony will give you a port.
By hopping your ships from port to port in shorter distances, you will avoid attrition of your fleets.
That's exactly how it happened in history. The Spanish established some "leap-frog islands" on their way to conquering the Aztecs in Mexico. Along the route, the Spanish ships needed to stop and resupply in ports like Canary Islands, Tobago, Bahamas, Puerto Rico, Cuba, Martinique, etc. A non-stop trip from Spain to Mexico simply would have been impossible, since the distance was so great.
About loading into fleets. You're doing it as the game intends it to be. You are exagerrating a bit tho. It only takes a month or two (maybe less) for troops to load from a port into a ship.
As for your land troops. Here is a tip, avoid moving them INTO a province that currently has snow (winter effects). That is what increases the attrition drastically.
if you think you have it rough with the attrition, just think about those huge Russian armies moving about in the frozen winters that blanket all of Russia....
there are some good FAQs here about attrition too, in the FAQ area.
last tip.... when you have named leaders around, keep in mind that they normally lower the attrition rates of the army stack they are part of. thus the presence of a leader will help to mitigate the effects of attrition. this is even more true since leaders tend to accompany LARGER armies.... and the larger the army, the more likely it is to attrition because the large army exceeds the supply limits of the province
oops. one more good tip.
in provinces where winter effects are severely attritioning some of your large garrisons, you should upgrade their fortresses as much as possible! this one is a life saver
the larger the fortress in your province, the better its supply.
better province supply = lesser attrition