So first, let me reiterate what you're saying in case I don't understand correctly.
You want to be able to use a trigger to select different CV voltages. When moving between those CV voltages you want the value to slowly creep to the next value and then remain there until another trigger is received.
So, let's break the problem into the two functions:
The first sounds a lot like a sequencer. You hit it with a trigger and it then moves to the next step that contains a different CV value. In my set-up, I'd use the Noise Engineering Mimetic Digitalis. It will rotate through 16 steps or you can set it to rotate through just four. You can use other lengths if you also supply a "reset" trigger... which you probably want to do anyways. Note: all three examples have reset inputs.
The great thing with this module is that it can store all of the values and you can recall them later. The down side is that you can't accurately change the values as it's running. But it has FOUR channels in it... so you can get crazy if you throw a switch into the mix.
My other option would be the Befaco Muxlicer. It has 8 faders that can output their own CV or take one incoming CV signal and attenuate it accordingly. The upside is that it's really easy to use and adjust on the fly. The bad news is that there's no storage. What you see is literally what you'll be getting. There's only one channel.
My last option is the Ornaments & Crime. It has a dual sequencer. It's more accurate to program than the Mimetic and can even store its settings. But you have to menu dive with a pair of rotary knobs. Not the worst interface... but some people just hate menus...
So whichever option I take... I can trigger specific CV voltages via a trigger.
NEXT... slewing between values.... SLEW RATE LIMITER.
Make Noise has the Maths module. One channel of this is PERFECT for the task. It offers rising and falling slope times as well as different scales of time (exponential, linear, log). Pros: dialing in exactly what I want. Cons: Expensive and a lot of rack real estate.
I also have an Intellijel Noise Tools unit with a generic slew rate limiter built in. I can substitute that for the Maths. Pros: cheap. Cons: only works in an Intellijel case with a 1U rack.
Anyways... that's how I would solve the problem within my own rack. Though there are probably other solutions that would work.