I don't think you'll have enough learning memory for those three devices.

The 9962 can have extra setup codes added via a .wav file that OFA customer support can play for you over the phone. Your three devices all sound like models for which OFA customer support would be able to find the right setup codes to include in the .wav file.

So if you have reasonable land-line (not cell or wireless or expensive international) phone access to OFA customer suuport, call them and ask them to "upgrade" your remote for those devices.

If you don't have reasonable phone access to them, your 9962 could be upgraded using JP1 software, which can construct .wav files (to be played by your PC's speakers) that are even better than what OFA customer support can provide. But that process would require quite a lot of understanding of the JP1 software. It's simpler to use the JP1 software if you buy the cable and use it that way than if you just use the (free) software via .wav file.