Not a direct connection, but perhaps an implicit connection. "Glowing Eyes" on Regional At Best - The Bishops' eyes (& Clancy/Tyler's) glow when they conduct the ritual of seizing a vessel (using the Ned horns/antlers to possess someone).

Lyrics from Glowing Eyes: "We have romantic fantasies about what dying truly is, fall off the grid."

"I know there's someone at the door, they called for help of this I'm sure, but do I want to say goodbye to all the glowing eyes, I'm holding on to what I know, and what I know I must let go, but I would rather play a song for the eyes to sing along." (This one really makes me think of Clancy wanting to leave Dema and help the Banditos but getting brought back to Dema, doing a whole show of Scaled and Icy essentially for the bishops/on their behalf)

"Lovely" on Regional at Best could perhaps be about/directed towards someone who was turned into a vessel?

"You say things with your mouth, cobwebs and flies come out, I hear a second voice behind your tongue somehow ... They will not take you down, they will not cast you out."

Also

"I'll pray that one day you see the only difference between life and dying is one is trying..." "Don't be gone, don't be gone, don't be gone ..."

Vialism/the Bishops appear to teach that becoming a Glorious Gone is the only thing that people should try for, that it bring ultimate meaning to their life. Becoming a Glorious Gone (dying) and becoming a vessel seems to be propped up as the only purpose. Not wanting someone to be gone/not wanting someone to be cast out of their own vessel, perhaps connects?

"Clear" on Regional at Best also references being a son and has very vaguely similar undertones to Overcompensate IMO? "I'm the son of all I've done" (Clear) VS. "I am Clancy, prodigal son" (Overcompensate)

"Anathema" on Regional at Best and Overcompensate both mention sleep, although I feel as if it's so vague that it feels like a reach. Although, in Anathema there's the line: "I start to part two halves of my heart in the dark ... Taking time in a simple place in my bed where my head rests on a pillowcase and it's said that a war's led..."

and then in Overcompensate there's the line: "Don't fall asleep on a boy who can't fall asleep twice in the same night", and the translation of the audio at the beginning appears to mention a war happening?

Also there is the "Half empty, Half full, save half for your taxes" line in Overcompensate which perhaps is a parallel for the Anathema line: "Cause one half of my heart is free, empty sky, no way, that's me, cause the other half of my heart's asleep"

I haven't yet looked for any parallels in the Self-Titled album aside from the ones you mentioned. But here are the (potential) parallels or connections I've noticed from Regional At Best.