In my experience Thief abilities hardly ever get used (unless and until they get a magic item they wouldn't otherwise be able to use), and when they do get used the differences don't really change playstyle. Non-thieves still climb and stealth and open locks; the Thief just gets some better rolls or and sometimes gets to do it without sacrificing an Action. Those are nice things and help statistically, but they are not qualitatively different. It is very rare (again, in my experience) that a Thief attempts something an Assassin wouldn't also try.
The Assassin has some nifty abilities for RP and interaction, but the right confluence of factors certainly don't arise every play session. And of course the Assassination ability is great statistically and gives Assassins extra incentive to get surprise and win initiative, but non-Assassins also want to get surprise and win initiative, so again it's a matter of quantity not quality.
And, again, I'm not arguing they are un-differentiated, just that I'd like to see more.
And what you talk about is precisely why I mentioned upthread that trying to use game mechanics to differentiate two subclasses is never going to work out the way someone wants. Because no matter how many new mechanics you give a subclass, they will primarily always use the mechanics of the base class. So they will always feel the same.
Using the example above... in combat, your Thief and your Assassin and your Swashbuckler will always feel the same because they each will use Stealth to gain Advantage on an upcoming attack, they each will then add Sneak Attack damage when they hit, and they each will then using Cunning Action to hide or disengage. It doesn't matter how many other abilities you give them... this is always how they will act in combat as part of a group.
Which is why the features of the Thief and the Assassin are primarily flavorful things that get used outside of combat to either give them more capability, or make them even better at something all rogues can do. And also why, as you mentioned above, they don't feel like they occur "often enough" to make them feel different. Because presumably you're looking at them each through the prism of mechanical combat use, as that's what usually occurs more than any other part of the game most often.
But there's nothing you can really do about that, short of actually completely re-writing the entirety of each of these subclasses to make them their own classes... so for example stripping out most if not all Rogue mechanics from either the Thief or the Assassin, and giving the other one a completely new mechanical change and method to combat. Because so long as the baseline Rogue abilities are the focus of how any subclass of Rogue fights... your Thief and Assassin will always feel like Rogues mechanically. Because that's what they are. (Which is why the class that has the most differentiated feel between their subclasses is the druid, because its their combat mechanics that change the most substantially between subclasses (where one uses spellcasting, the other uses melee wildshape.)
Other than that... your only other options that I can see are either to find/download complete 20-level class write-ups of various classes to use in place of many subclasses (so find if someone actually designed a 20-level Assassin base class and use that, while using the Rogue as your Thief)... or else rename some subclasses differently to remove the more esoteric naming conventions to other ones that you want more (so for example, rename the Order of Shadow monk the 'Assassin', and remove the Assassin subclass of the Rogue altogether... thereby making the Thief and Assassin feel completely different because they are now baseline two different classes.)
At the end of the day, you can try to make the differences feel more pronounced between the subclasses by adding more mechanics... but so long as the main thrust of most of the game mechanics remains combat-oriented, and most combat mechanics are given by the base class and not the subclass... I think you're going to have a hard time hitting the mark you are aiming for.
Good luck!