Also I was wondering if it's possible to get motion blur on the ends of splines meshes that grow between bindings?
There are various ways to approach this...I'd have to see the file to add further suggestions.
Hmm, yea...looking at your file, the way you've set it up there's not really an easy solution. You'd have to try a totally different approach that doesn't leave any frames where the splines don't grow. You mention interpolating them between the gaps, but there's nothing to interpolate them towards since they extend to the last particle in the spawn group already....and based on how you setup the binds and such, not even the parent particle offers a smooth location to interpolate towards. You can switch the Spline Paths mode to "siblings" and enable "connect to parent" to see how it looks when the spawned particles include the parent in their spline generation...but it looks weird due to the spawned particles moving past the parent's location in many instances.