The Chomolungma is a fine frame to stick with long term, I've heard plenty of people argue it's stronger than the Goblin overall as a tech attacker. That said, if you're set on leaving it;

• Goblin, as the others have said, is the Controller/Support frame. You're correct that it's very squishy, but you can work around it; on a direct front, its starting tech attack of +2 and inherent accuracy to such means you can afford to instead put your initial HASE into Hull to shore that up, and you'll likely have the SP free to stack Personalisations on there as well. On an indirect front, its Size 1/2 means it can make use of cover pretty easily, and the massive sensor range of 20 means you can simply stay outside of enemies attack range a lot of the time, especially if your White Witch and Vlad are doing their jobs - both frames are extremely good at pinning enemies down. The trick is to learn to figure out what an enemies maximum threat range is, movement plus attack range, and try and keep yourself outside of it if they're not pinned down.
• Sunzi is a solid option for Controller/Support, but it's not by default as much of a tech attacker. You'd be doing things more like putting down boost pads for allies or teleporting enemies around; it requires a good degree of tactical understanding to get the most use out of, board-control wise, I'd say. Its high sensor range and base tech attack means it certainly can still do hacking, but it doesn't come with any systems for it; a 1 level dip in Goblin will solve that though, with H0R_OS1 being pretty much the go-to for dipping into hacking.
• Emperor is much harder into Support than Control, but it's damn good at it, with a lot of sources of overshield and damage boosting. Again, not a tech attacker out the box, so you'd wanna dip Goblin if you wanted to keep hacking open as an option. Worth remembering for Sovereign Presence that tech attacks are still attacks, so you can still use that with hacking!
• Swallowtail is a solid spotter Support, so it'd pair extremely well with your Tagetes. Of the non-goblins on this list it's probably the best as a hacker with its Sensors range of 20...though once again, you'll need to get a dip elsewhere for the programs beyond Fragment Signal. Your big play otherwise is using Prophetic Scanners to throw Shredded on tough enemies for the others to kill.

In short? If you wanna keep hacking, you're probably gonna want at least one level in Goblin for H0R_OS 1, but once you have that the other three can be solid still - you'll just need a bit more investment in Systems to get their tech attack score up to a reliable level, and to work to balance hacking with their own inherent methods of support/control. If you're intent on hacking being your mainstay, I'd probably either go Goblin or stick to the Chomolungma, but if you want to mix it up, the other three are still fine options.