In general I think it's a bad idea to change {.i} so that it doesn't always start a new sentence. The major problems are that it deals a heavy blow to the whole concept of elidible terminators, if you can't "just start a new sentence" to get out of a deeply nested pit of abstractions; and it means it's no longer possible to quickly scan a text for {.i} to separate the sentences -- you need to parse the entire text to find the sentence boundaries. So I would definitely favor a solution for the first problem that doesn't change the grammar so drastically. (Not to say I'm against new grammar in general, of course! But I find severe disadvantages with this particular proposal.)
The bonus problem is not so hard -- you can use {zo'u} as la .guskant. said, or indeed plain tu'e/tu'u, or connect the sentences with {.ije} or {.ibo} to suggest close binding.
- mu'o mi'e la durkavore
P.S. It occurs to me that la zipcpi's "super-terminator" {.i'au}/{.iau}, which I previously dismissed, could cover some of my above objections to changing the meaning of {.i}. However such a super-terminator has yet to be formalized and it seems silly to introduce the change if we need an escape hatch cmavo for the common case!