No, there's no reason to wait to use the compost that is ready to use now. Different inputs to the compost pile take different amounts of time to break down.
We've been actively composting pretty much everything that can be composted here on our farm for the past 10 years or so and about the only thing that I'll do to twigs is cut them down a bit to make them more manageable in the compost pile (easier to turn with a fork) and to increase the surface area of the material. I don't have a chipper-shredder but I might be inclined to use one if I did.
For inputs which are slow to decompose, I'll just leave them in the compost bin and, over time, they'll break down. Our bins are dynamic things that are always "cooking away" at something.
To simplify this process, I use a coarse screen (1/2 inch hardware cloth or maybe some chicken wire) to screen out the larger chunks. I don't worry particularly too much about uniformity in size of the compost, other than to screen out the pieces that need more time.
You can increase the decomposition rate by decreasing the size of the carbon-rich materials like twigs by chipping them up or breaking them up. Again, it's about surface area. Chipped/shredded twigs will break down faster, all things otherwise being equal.
Since you've said that much of the compost has broken down nicely, it is clear that the decomposition process is working well. Again, the carbon-heavy materials take time sometimes, particularly dense materials. I've got one bin that has pruned twigs from last winter in it and they are partially broken down. I just sift those out and throw them back into the bin.
Aside: It wouldn't be terribly awful if the twigs/shells weren't completely broken down and they ended up in the garden. They'll break down there too. But I tend to leave the materials that aren't quite done yet in the piles.