Points arising.
Rough running pump. Looking at the photo's in one of them it does look like some of the commutator segments are "blued" on the ends, which suggests a lot of heat so I think that it is possible that some of the armature maybe open circuit or high resistance. I certainly know from my "go around" with the pump that the motor will still spin and pump with brush problems and the odd winding "missing" on the armature.
Pump motors seem to be the same on all models however the firmware in the BHI does appear to have minor differences when I changed mine for one purchased from a scrapper I found that while the suspension stuff worked fine it didn’t appear to provide the correction signals for the Xenon headlights. I ended up using the "new" pump and the original electronics.
Reservoir cap.
Seems to be "one way" i.e out. What the logic is is still unclear to me at least, the following is just my thoughts and should not be taken as a definitive " this is the way it is".
The hiss that you hear when undoing the cap everybody assumes is air hissing out, however could just as easily be air hissing in, I've never been able to work out a viable way of proving it one way or the other

. However my belief is that when the system was designed it was designed as a sealed for life system and in order to achieve that, particularly if the original oil was envisaged as LHM (speculation) then the exclusion of air or more pertinently water would / should have been a major consideration.
As those of us who have had traditional Cits know, LHM over time (several years!) does sludge and as with all mineral oils water is a major contributor to this process so preventing humid air sitting on top of the oil would / should have been a design consideration to reduce sludging and resulting filter blockage.
The introduction of LDS an oil which is identical in specification to LHM with the one important difference that it is a synthetic based oil and not mineral based would have made this particular design requirement even easier to achieve as it is my understanding that synthetic based oils are generally less hygroscopic than mineral based oils so the use of LDS in a sealed system would in theory anyway allow a closed system to work for many years without the need to drain and clean the hydraulic system, and the filter which is in the pump would outlast the pump.
I don't think that it is a good idea to draw parallels between the older LHM based systems and those on the C5 / C6. The older cars were not designed as a maintenance free sealed for life system and the hydraulics had to look after everything, brakes (heavy thermal cycles) and DIRAVI steering ( high flow and pressure) as well as suspension.(low flow high pressure). On the C5 and C6 the hydraulic system only does the suspension (low duty cycle) the power steering uses a separate pump.
On the older cars the height correctors were mechanical valves with a pressure and return line, further the pipe run from the height corrector to the strut was relatively short and of small diameter steel so in terms of getting air out of the system a couple of cycles of Citrorobics would be able to move air laden oil back to the return line on the height corrector.
However on the C5 the equivalent mechanical part of the height corrector is at the front of the car with in the case of the rear suspension a long pipe run of relatively large diameter rubber pipe to the suspension cylinders so it seems to me that it is quite possible that cycling the suspension may do nothing more than move bubbles of air up and down the pipe.
However it does occur to me that a partial vacuum in the reservoir would help de-aireate the system and I can't help reflecting on the fact that there are bleed valves built in close to the suspension units, I am sure that the designers put them there because they knew they were needed.