I think scotch wrote a post on replacing the plastic filter with a fine brass gauze.
Yes. But there is really no magic to it - just put a piece of mesh around the tube and secure it with a wire. The reserve is just a hole, you'd need to stick a piece of tube in it as well and then wrap it. The mesh around the main tube will give that protection similar to the original screen, but leaving the reserve hole as is will not protect that one. Best never switching to reserve in that case and monitor the miles. Maybe disconnect the fuel line and drain some fuel to clear anything from the bottom.
So... this way or the other - why not. But with an external filter added, it's proven to work just fine. There is no petcock or mesh on my Vmax, and that's a 1200 cc. Just an external in-line filter by factory design and works just fine. Even with the fuel line smaller than that on KZ1300, there is absolutely no problem with the flow. It pulls like a train when the v-boost kicks in at 6000 rpm, and that is when each one cylinder gets mix from two carburetors at once.
I'd say just remove the screen with all it's skeleton frame, clean the petcock and install as is. Then fit an inline filter - cheap an easy to replace.
I'll post a photo and some detail if you choose to go that route.