我觉得应该是a long slow process，因为 slow 与 progress 关系更紧密——是因为慢才导致长，所以 slow 紧挨着名词放，long 放在稍远的地方。如：

the long slow climb out of the recession 经济衰退期后长时间的缓慢复苏 

He took a long slow breath, inhaling deeply. 他缓缓地深吸了一口气。

Getting fit again has been a long slow process. 恢复健康是个漫长的过程。

They began the long slow haul to the summit. 他们踏上了攀登顶峰的漫长行程。