- 1. e4 c5 2. Nf3 e6 3. Nc3 Nc6 4. Bb5
Black can hold back with Nc6, but even if he doesn't, I don't really see what bite the Rossolimo has when black can play Nge7.
- g3 -Systems
I don't usually play fianchetto systems in the open, but I might look into this.
- 3. d3 seems just like a worse closed Sicilian (without f4) to me, indeed rather wimpy. I might give 3. b3 a go.
- 3. c3 and c4
Indeed the given lines look undesirable.

How about some gambit lines? Can you favorably transpose to some Morra or Wing gambit line? I figured the e6 player wants a safe and secure game and I'd like to not comply with that.

Well 1.e4 c5 2.Nf3 e6 3.Nc3 is one option:

a) 3...Nc6 4.Bb5 is a type of Rossolimo;

b) You could try systems with 4.g3, where you hold back on d4. I believe this was recommended in Chris Baker's "Startling Repertoire" book. This might frustrate some Kan players, but 3...Nc6! 4.g3 d5 5.exd5 exd5 6.d4 Bg4 is just awkward. (I think Baker recommended 4.Bb5 IIRC.) The idea is to transpose to fianchetto Open Sicilians, but to limit Black's options along the way. It might be effective against alternatives to 3...Nc6.

Larry Kaufman recommended 3.b3 (and 3.d3 as a secondary line - which IMO is a bit wimpy ) in his repertoire book. It's probably one of the anti-Sicilians closest in character to the Open Sicilian. White often aims for a Maroczy bind position with c4 and d4. That's an easy short-term solution.

If you like to play against the Scheveningen, you may want to consider the a3 idea against the Taimanov in the Dangerous Weapons series. This is not found in Delchev's book, so it could easily trip up a lot of Taimanov players.

Lastly, there's also 1.e4 c5 2.Nc3 e6 3.Nge2 in which it's useful to have some knowledge of the Closed Sicilian. Fischer played this against Spassky in their 1992 match. In this case, after 3...Nc6, 4.g3 is not so bad and this returns to my contributions to the Closed Sicilian thread.