Hi,
Daniel I have downloaded files you provided.
First of all I want to thank you for an effort you put in this assembly.
I was (in the beginning) also surprised how stable it is (seemed to be) in a state you made it.
I will now refer to mouse driven assembly:
1) In this assembly and in any of flexible components there are NO constrains that use limits. All constrains in top level assembly are defined as of fixed value, and range constrains in flexible components (max/min extension of props) are suppressed.
(Non of them can be used in order not to crash this assembly).
This kind of limitation is rather not acceptable for me because I very much need constrains to restrict movement of parts in my assemblies in certain limits, to see right away if something will work, not having to remember to constantly make measurements if in current state I am not exceeding max jack stroke for example.
Apart from static assemblies I also have many designs in witch I design equipment to move or manipulate objects (like bridges for example). In such design I have an object that will be moving or will have to have certain displacement and during its movement it will be in all intermediate states.
If I then have some construction or device I must check if it will not be in the collision with a moving object in all situations and possible layouts of equipment, also I need to check if equipment or construction I am designing will allow for a desired operation to be performed successfully.
Therefore I always use mouse dragging technique + limit constrains.
This works 100% fine if I have all moving parts on top level assembly. In such case Inventor has no problem with limit constraints and moving elements.
Also I can apply any constrain I want and if it causes collision I am getting inconsistent constrain error message instantly, also in any case this will not destroy assembly.
If any of constrains defined in top level assembly, is changed to constrain using limits, this assembly starts to crash very quickly, and Design doctor throws usual inconsistent constrains error messages, indicating constrains within flexible components as conflicting.
In such state assembly is forced in to positions against defined constrains, and at some point becomes not possible to repair.
On following picture I show one of layouts constrain solver forced this assembly after turning one constrain, as using limits, and trying to drag some parts with a mouse.

There is no way assembly can be repaired from such state. Only solution is to rebuild it from scratch deleting all flexible components.
2) even in the assembly as you uploaded, Inventor is not capable of driving constraints defined at top level.
Trying to o so instantly causes an error. Assembly is not crashing but constrains solver cannot solve intermediate states during driving a constrain.
Second image shows error message from constrain solver when trying to drive one of the constrains on top level.

3) I quite quick found out that this assembly is not 100% stable and crash proof.
I tried to play a little bit with this Rama_Insert_6 constrain and put values from range I was intend to drive it, to find out if inventor can solve this or not.
Accidental I put value of 600. I got warning.
If I chose to cancel it is safe.
If I chose accept (because this could be the value I needed (in some other case) and wish to correct other constrains after) this assembly is destroyed. All flexible members are forced into positions against their internal constrains.
But funny thing. I managed to get 600mm value for this mate only needed to approach this value slowly putting 200, 300, 400, 500, 550 ....
So Inventor obviously is not capable of solving this assembly 100% stable. And there are usual errors that I so often fight.
Below is an image of the assembly with 600mm for mentioned constrain.

And an error message from another attempt to put 600mm value in this constrain

+ result after "Accepting"

Some parts I am not able to find.
As for parameter driven assembly you uploaded, I have not yet had time to look in to it in detail.
But from the first look I got the feeling this is not the approach I expect. Anyway I will look in to it.
So summarising my findings based on assembly you provided I must state that:
1) restrictions (I name in the beginning of this post) n to make it work as you showed, are not acceptable for me. This is totally not what I expect from using flexible assembly.
2) Assembly build following this restrictions is also no 100% stable and shows usual problems with flexible assemblies (the once I usually encounter).
As other flexible assemblies (I know) this assembly can easily, by accident, or at least not intentionally, be forced in to positions that are against constrains defined in the top level assembly as well as these defined in flexible components. Also it was shown that inventor is not capable of solving this assembly in 100% stable, proper way.
Considering all that I, with regret, must once again say that, in my opinion such thing as flexible assemblies in inventor is not usable and should be fixed.
Specially that it is easy to prove, that the same layouts of parts, are solved properly if all moving components are inserted directly in to top level assembly.
So problem lies strictly in how, so called "flexible" components, and their constrains, are promoted to to level environment.
Cris.
in case you agree flexible assemblies do not work as they should, here you can support idea to fix them: Fix Flexible assemblies