Do you have the 20XX training mod (not to be confused with the Tournament mod)? It randomizes teching (to tech or not, as well as teching in place or rolling either direction) as well as DI (granted it has a huge bias towards cardinal directions due to how melee reads the controller input). While it doesn't help you *read* you can use it to craft a personal flow chart to catch specific options.
I'll give an example to help explain what I mean:
I've found that I can cover most options after a down throw to dash towards my opponent after the downthrow, and then follow the tech; however, it's hard (and possiblyimpossible for some combinations) to react to a missed tech, or a DI away roll away. So for general purposes, this is pretty good, cause it covers more options.
However; if you expect your opponent to DI away and tech roll away, you can work on another system that can catch that, and as many other options if they chose something other than this.
EDIT: I didn't read your entire post, but I'm certain that you could catch DI away and tech away, but it would be more of a hard read, because you kinda have to dash asap and keep running to catch them. That said, you can practice your reaction by using that tactic and trying to adapt it to what the computer does in 20XX and see what options you are able to cover with your reactions.
The idea here being that there is not one system that catches everything well, but you could develop and practice multiple and use your observations to inform your decisions.
A caveat though:
DI away + tech roll away gives up A TON of stage. As long as you cut your opponent off, that in and of itself is a victory in terms of stage control. A tech chase doesn't have to grant you another grab to be successful. As long as you can place yourself in such a way that you aren't vulnerable, if they gave up all that stage you win.