As long as your platforms — Tightknit and others — would work the same in a Slack Connect channel as they do as a regular public/private channel, then I'd recommend a connect channel. Reasons:
Communication and access is a key part of an early access program.
Remove barriers for your internal teams to collaborate with customers in the program, as well as make it easy for them to use their existing internal tools for logging issues, feedback, etc. + easy to add folks to the Slack Connect, if needed.
Deliver your employees a badge for the close and/or GA of the pilot along with members to bring the two groups together in the moment to celebrate the launch.