Hi Mark_S_Johnson,
Asking for simple and procedural solutions… : Not to my knowledge.
The first problem is given in the fact that the child objects are cloned. Which means that the child is processed and then cloned. The cloning ends the process of anything, as it is a copy. The work around is possible with applying Hair in some cases to the overall group of clones, if they are stable in count.
Since we have with particles often a highly changing number of “clones”, this process isn’t working.
The idea would be to create a lot of single units of this, e.g., a null as parent, holding the Hair and the object), and transfer then the position (via iteration) to those single units. The problems here, the particles die and change so the index number, and with that the index is not stable to a position. One could think to create a matrix with those positions and transfer such thing to a spline or something like that. But there is, so far my experiments, always some movement, which affects the dynamic of Hair. Since the number is changing as well, the reminding objects needs a special treatment. This could be a transfer to the needed emitter position while invisible, to calm down, until they are needed. There are options to give each particle (Thinking Particles) a unique ID. But there are more problems than that.
Given the Dynamic effect of the object as well the Hair Dynamic, placing them at the same position, while in waiting position seems problematic. Dynamic solvers needs to be turned off, switching them on might cause movement …
Given the use of standard particles, the access to the inner working information seems quite difficult (C.O.F.F.E.E. or Python). So Thinking Particles perhaps.
Much easier seemed to be the way to Trace the Particles via MoGraph tracer, and have then the before mentioned “units” traveling along such Splines. Since they produce per frame one vertices, the only problem is that these vertices start with the born event of a particle, and not with frame zero.
I have no solution that works with a few clicks. Sorry.
All the best