Not a DB user: just a few questions and hints ...
By "real-life experiment", do you mean a closely-controlled lab experiment akin to a guarded hot box setting (e.g. no equipment gains, minimal envelope gains)? It will likely be harder to maintain constant temperature and humidity in a more conventional setting. And in either case, I suspect "constant" is short for a narrow control of heating/cooling: 23°C +/- 0.5°C (or similar)? Same for relative humidity control?
By controlling "humidity via the heating and cooling system", have you added AHU humidity control (based on EnergyPlus' de/humidifiers and suitable humidistat control)? You can certainly define minimum (humidifying) and maximum (dehumidifying) relative humidity setpoint schedules. That's the first thing I'd like into (EDIT: applicable only for Detailed HVAC mode).
If ~instantaneously achieving a relative humidity of 95% (!) is beyond the scope of the humidifier model, then my second thought would be to explore Process Gains, which harnesses one of EnergyPlus' Equipment classes (not sure which one), e.g. Electric, Steam or Other. You would want to maximize the latent fraction, minimize the radiant fraction and zero the fraction lost. You can associate a schedule to such process gains to match the sudden humidification/dehumidification events you're seeking to model.
You'll likely need a few trial-and-errors iterations to nail down the expected behaviour.
EDIT: Based on your follow-up comments, I suggest the following edits to your initial question:
The challenges you're facing with humidity control have more to do with setting the right variables in DesignBuilder than having to deal with a virtual test bed setup, or even temperature control. I suggest you revise the title of your question, e.g. "Scheduled %RH? (DesignBuilder)". Hopefully this will attract (more) experienced DesignBuilder users, maybe even DesignBuilder developers.
If you run an UMH search for "humidity designbuilder", you'll come across quite a few relevant posts. I suspect a few are worth the read.
From your description, I take it you've opted for Simple HVAC (i.e. IdealLoadsAirSystem) - not Detailed HVAC (plant/loop)? This should be made very clear in your initial question, even your title e.g. "Scheduled RH% : DesignBuilder (SimpleHVAC)?". The available options and subsequent steps to follow for humidity control are quite different between both options.
From the previous link and the following, I take it that one can't schedule de/humidification setpoints using the Simple HVAC option: one can only define a constant minimum %RH for humidification and a constant maximum %RH for dehumidification. That may be why DesignBuilder doesn't import the de/humidification schedules you've provided in your edited IDF. If you upgrade to Detailed HVAC, you should be able to schedule both de/humidfication setpoints.
