As much as I love RE3 and hate to bash it, if your complaint about Nemesis and Mr. X is that they're too persistent and interrupt the slower, more deliberate exploration you normally do, RE3's Nemesis honestly isn't really a major threat and isn't comparable to the RE2 remake's vastly more aggressive, persistent, and unkillable version of Mr. X. He's basically a more persistent Mr. X from the RE2 scenario with more dangerous attacks, but every single one of his appearances can be memorized, and he only appears in specific rooms in each appearance, disappearing and effectively ending the encounter when you leave the assigned area he can appear in. In the rooms he's barred from entering, it will still play his theme music if you're still actively being pursued by Nemesis (i.e. the current encounter is still active because you haven't run far enough to have considered to have "escaped" him).
For instance, in the first encounter outside the RPD, the encounter ends if you enter the RPD, or run back down the street (where Nemesis will appear as soon as the gate is off-screen) and get to the area where the Save Room is.
In his second appearance, Nemesis will show up in the RPD and follow you from room to room, generally being allowed to enter every room except the tiny room with the vaults/lockers (and possibly the upstairs Star Office and the Press Room, but those are purposefully going really out of your way instead of the obvious getting the hell out of the RPD). Bare minimum is two rooms in the encounter, the room at the foot of the stairs, and then the office Marvin's body is in, both of which are easy to run from. If for whatever reason you want to go back and explore the RPD more, you can just end the encounter with Nemesis by running to the main hall (or possibly outside the RPD/outside the gate, can't remember what room triggers Nemesis to vanish from encounter #2), and then you can go back and explore the Nemesis-free RPD all you like.
The subsequent encounters all follow the same pattern, with him only following you in a specific set of rooms and the encounter effectively "ending" with him disappearing if you go back once you've gone far enough away to end the encounter.
This of course doesn't include the 3 mandatory fights you can't run from: the Clock Tower battle, and the final two fights in the sewage facility.
Unlike RE2's remake, where Mr. X follows you pretty much the entire time you're trying to explore the RPD once he's been triggered, RE2 and RE3's big bad trenchcoat dudes can both be dealt with by running from them or killing them, and ending the encounter either way will then allow you to go back and explore at your leisure as much as you please. RE3's Nemesis really isn't that much of a threat when you work out how he functions, which is essentially as a multi-room boss fight that you can run from.