Okay, it MIGHT be possible to make this work without breaking the setting too much.
Basically, what you're wanting is: (I think)
A) Reveal more about the gatebuilders/gardeners without meeting them. Currently, as it stands, you do it, but not nearly to the extent that you multiply existing questions and raise disturbing new implications in that all the worlds explored are empty/ruined, and the only thing found is a single settlement so far.
B) Expand the frontier greatly. Kind of pointless, since there's hundreds of stars within a month's travel of Earth, so dozens of gates is ludicrous overkill.
C) Force an encounter with aliens.
I think you could get away with the current story with a bit of work. Have it be that the exploration wakes up the local gate network cluster AI. After explorers start coming back from the various destinations, probing the system gets rejected by the gate, with it probing the ship systems for language files. It proceeds to respond, saying that the explorers are violating primitive species protection zones. One or two are left open, like the Silver Moon one with the spire, which the gate refuses to directly answer on, but but the identity code suggests it was a hub station that was abandoned. (Impact/got uneconomical to leave people there). When prodded again on the subject, it makes another gate available, which leads to a system about 50 lightyears from the Squiddies (which is determined from seeing engine trails or picking up transmissions at long range).
Less icky trap sensation, but depending on how you frame the response, you could keep from implying that the gatebuilders/gardeners were a happy-go-lucky UFoP. It could just as easily suggest that they left because they realized that a lot of planets along the spiral arm were developing sentient life, and they didn't want to put up with it, and leave it open enough that there's questions without those questions being annoying or setting-breaking. And, we get to play with the Squidleigh without there being a crazy travel time, while leaving the timing of our encounter up to the authors.
Basically, what you're wanting is: (I think)
A) Reveal more about the gatebuilders/gardeners without meeting them. Currently, as it stands, you do it, but not nearly to the extent that you multiply existing questions and raise disturbing new implications in that all the worlds explored are empty/ruined, and the only thing found is a single settlement so far.
B) Expand the frontier greatly. Kind of pointless, since there's hundreds of stars within a month's travel of Earth, so dozens of gates is ludicrous overkill.
C) Force an encounter with aliens.
I think you could get away with the current story with a bit of work. Have it be that the exploration wakes up the local gate network cluster AI. After explorers start coming back from the various destinations, probing the system gets rejected by the gate, with it probing the ship systems for language files. It proceeds to respond, saying that the explorers are violating primitive species protection zones. One or two are left open, like the Silver Moon one with the spire, which the gate refuses to directly answer on, but but the identity code suggests it was a hub station that was abandoned. (Impact/got uneconomical to leave people there). When prodded again on the subject, it makes another gate available, which leads to a system about 50 lightyears from the Squiddies (which is determined from seeing engine trails or picking up transmissions at long range).
Less icky trap sensation, but depending on how you frame the response, you could keep from implying that the gatebuilders/gardeners were a happy-go-lucky UFoP. It could just as easily suggest that they left because they realized that a lot of planets along the spiral arm were developing sentient life, and they didn't want to put up with it, and leave it open enough that there's questions without those questions being annoying or setting-breaking. And, we get to play with the Squidleigh without there being a crazy travel time, while leaving the timing of our encounter up to the authors.