True. But most Members of Congress don't have the resources a President has to filter and hide information inside of their exempt bubble. A President filters the vast majority of his outside communications through his staff. That makes the connections much harder.

Is that first claim true? Certainly they don't have the resources of a President, but all Members of Congress have non-trivial staff, and will conduct most of their outside communications through that staff. No Member is so deficient in staff that they wouldn't have the personnel to have all communications with a potential briber go through a staff person - though that seems to my mind to be the least likely scenario for how a bribe would go down.

In the two recent cases against Menendez and Cuellar, the DOJ was able to get search warrants for their homes to generate admissible evidence. Good luck getting a search warrant for the White House, never mind the fact that the DOJ won't even begin an investigation until the president suspected of a crime is out of office.

You'd never need a search warrant for the White House. As you note, the DOJ will not begin a criminal prosecution against a sitting President - we're only talking about criminal prosecutions against a former President. All documentation/evidence would be removed from the White House and would be in their private residence, just like the situation with Menendez and Cuellar. Or else it would be left behind in government records, in which case the DOJ wouldn't even need a warrant - they'd just ask the current custodian of the records to send them a copy.

But what about the Jan 6 case? That case depends more heavily on testimony from those inside the White House. Could Hatch Act violations pierce the wall of immunity - turning conversations between President and official staff into conversations between a candidate and his campaign staff?

Not sure how that would be necessary. Again, none of this is privilege, but immunity. If the act is immune, then it doesn't matter with whom the President had the conversation about the immune act - the conversation would not be admissible. To use the legislative example again, if Congressdude Jones has a conversation about his thoughts on an upcoming vote with his wife (or his uncle or his golfing buddy or whomever), those conversations can't be used as evidence against him in a criminal trial - because he's utterly immune from any sanction or punishment for casting his vote a certain way, which means that evidence about his motives or reasoning or thoughts about casting that vote is not admissible. It's not contingent on the conversation being an official act, but that his vote was an immune act.