400 possible warnings per week is not too much, for speaking about data overload (especially if you operate 66 satellites). Imagine a doctor complaining about having 400 patients every week.
400 warnings per week are less than 6 warnings per satellite per week. You would on the average deal with one collision warning per day, for one satellite.
The space debris warning are part of normal everyday operations and if you don't have the employees, to deal with them, you leave a very bad image of your performance. Blaming the USSSN for not being accurate enough with their warnings, is stupid. The USSSN watches a few thousand objects in Earth orbit and you can be lucky that they issue such warnings to you, instead of you being forced to watch for your investment by analysis the TLEs of all dangerous objects.
After all, it is just like in Air Traffic. If a ATC issues a collision warning based on his rough radar data, this does not mean that there is a dire collision risk. But you need to deal with it, look at your own state and do the decisions that are required. This does not always mean that following the ATC is the best way (look at the Bodensee collision), but their recommendations have weight unless you really know better.
Sorry, but I don't accept this kind of excuse. If the USSSN already reduces the work load for you, by issueing such warnings and do the calculations for you, you should not complain about a too high workload.
If satellite operators want better service... they can buy it. Either by employing their own engineers for this task, or by contracting a special company for such analysis. I am pretty sure such experts exist not only inside CNES and the rest of ESA.
I would estimate, that if you can get accurate state vectors from the satellite operators and other information (propellant resources, for example), you could deal with the 400 warnings every week with about 5-8 engineers, who do nothing else but that.