A challenge, yes, but an insurmountable one? No. There is no fundamental need to keep the written form of a language across various dialects unified. If people can understand each other's accents and dialects when speaking, they can also understand those same differences when expressed through writing (assuming that the writing system is capable of expressing those differences accurately enough, which the current English orthographies are not). In fact, writing in your own dialect and accent in informal contexts (e.g. on social media) is quite common in some language communities, and it doesn't particularly hinder communication. Thus, you could theoretically let the spelling vary by dialect and everything would work out just fine for the most part.