I think what you're describing is called "overload recovery", it's a general problem with all opamps (not just the ones in the DS1054Z).
Operational amplifiers started being used in oscilloscope front ends to control drift of the input source follower starting in the early 1980s and those oscilloscopes did not have this problem. Unless this particular Rigol is broken, what is going on is due to a design flaw.
Really? Most manufacturers have discussion of this on their web sites, eg.:
Old oscilloscopes did not have the magnitude of the problem displayed by this Rigol. Other modern DSOs do not have the magnitude of the problem displayed by this Rigol. 100s of microseconds of overload recovery (1) time for an overload of only 9 divisions? Really? I have to overload my 2232 by 72 divisions to approach the same effect which is two more increases in vertical sensitivity and the 2232 has what I consider terrible overload recovery. The Rigol overloaded immediately.
In the past they made special vertical amplifiers which could recover from any overload within a bounded time so for instance a 10 volt overload at 1mV/div or 10,000 divisions (!) required a recovery of 1 to 100 microseconds depending on the accuracy required. (2) But even normal oscilloscopes did much better than the example here.
https://www.tek.com/document/competitive/overdrive-recovery
"404 not found" "Page not found"
Which is typical of Tektronix's broken web site.
https://www.keysight.com/upload/cmc_upload/All/ADMF2008_SwitchingModePowerMeasureUsingScopes.pdf
"Some oscilloscopes are known to have better overdrive recovery than other oscilloscopes."
This is true.
"However, all oscilloscopes are vulnerable to an overdrive state, so it is best to avoid this condition if possible."
This is completely false. For instance sampling oscilloscopes are completely immune to overload short of damage making them uniquely useful for measurements where this is important.
The Rigol and any other modern DSO should be able to make this measurement despite overload. The overload recovery demands in this case are not in any way extreme.
(1) It really should be called "overdrive" recovery. Overload implies destructive levels.
(2) At this level of overload, thermal effects come into play so the amplifiers recover within a microsecond but it takes 100 microseconds for the thermal effects to dissipate. These thermal effects are the same ones which limit settling time in precision operational amplifiers.