I don't really think there is a Q, and instead think that Luke had access to proto-Thomas and Matthew had access to both Marcion's Luke and proto-Thomas, with a final redactional layer of Luke-Acts potentially having access to Matthew in turn.

The Synoptic Problem is a huge swamp, but I'm a big fan of considering redactional layers for at least Mark and Luke.

Most Biblical scholars didn't really want to give Thomas any credibility early on, and that combined with the tautological dating of anything with an apparent whiff of Gnosticism to the 2nd century led to scholars bending over backwards to ignore it in favor of other theories.

But there's a notable overlap between Thomas and the letters from Paul to Corinth including reference to things they have written or are saying (who he later accused of accepting a different version of Jesus from what he offered), and there seems to be direct dependency of both Luke and Matthew on it here and there, and now we've even seen with Oxy 5575 that in the 2nd century sayings unique to Thomas were being woven together with Synoptic sources as if of similar credibility.

I think attitudes about this text will change over time, but it will still take a while as it's a slow moving domain and there's a lot of legacy bias against the work.

Edit: Also, the secretive parts of Thomas are less than you might think and I suspect are a 2nd century layer added on to the core work which was also when the association with 'Thomas' was added. For example, all the "two ears to hear" would indicate public statements given saying 33 (even more anti-secret than the Synoptic parallels) in the work, not secret sayings. The secrecy stuff was likely reactionary to the canonical claims of secret explanations, i.e. "no, we have secrets too!"