Would SWT's 455s and 456s potentially be able to work with 319s in service without any modifications?
No, quite simply. They could couple mechanically, but that'd be it. Beyond that, you'd need to modify the 319s to have the old SR multiple working cable (can't remember how many pins off of the top of my head) as well as the air hoses. Either that or run them on their own, but I can't really think of any services they would be suitable for. You could use them on a new local service around the south coast,
eg
Portsmouth Harbour - Lymington Pier
Portsmouth Harbour - Bournemouth
Portsmouth Harbour - Basingstoke
etc
but, like I said, I don't really have any idea if a) there are paths, b) there is demand, c) would it be within the franchise specification
To be honest, I think that the best bet for the 319s would be consolidating them at one operator, such as Northern, subject to a large scale refurbishment - new traction , new interior, air conditioning, removal of 1 carriage etc. This may have to be done at the expense of the 323s, but with a timetable recast, the effect of this could be reduced. I am also thinking that using the 319s at southern as the coastway fleet would be a feasible idea, which would allow the retirement of 313s and the movement of 377s to other mainline or metro services, although again, a proper refurbishment would be in order.
With my blue-sky thinking hat firmly wedged on my head, I'm also wondering about what could be done if they were shortened. There would be a large amount of mk3 EMU bodyshells knocking around, from the 319 shortening and the movement of 7 321s to Scotland. It might be feasible to construct some driving vehicles with the necessary traction equipment which could then be used on other routes.