Answer: Probably not. Let me explain, with references to the 4th edition of my book, Who's the Employer?. (Subscribers can click to view online the text of these references.)
Let's start with the effective date issue. When the IRS proposed its 403(b) regulations in 2004, it expected to get a few comments, make a tweak or two, and put out final regulations in 2005 with an effective date of January 1, 2006. Instead, the IRS was flooded with comments. The Treasury just missed issuing the 403(b) regulations by the June 30 end of its regulatory fiscal year. The latest rumors say the regulation might finalized this September.
Hence it is highly unlikely that the regulations will be effective in 2007; my best guess is that they'll have an effective date of January 1, 2008. (I hope that the 414(c) portion of the regulations will be tied to plan years, but we'll see. [Q 12:11.]) Of course, there are no guarantees that the final 414(c) regulations will follow the proposed regulations.
But let's say that they do. How would they apply to your situation? Frankly, they wouldn't. Here's what comes closest:
If you have 2 tax-exempt organizations and at least 80% of the board members of one organization are representatives of or controlled by the other, then the 2 organizations would be under common control. [Q 12:12.] An individual is a representative of an organization if he or she is a director, trustee, agent or employee of the organization. [Q 12:13.] Overlapping board members therefore are representatives of both organizations.
The proposed regulations state that, in general, whether an organization controls a board member of another organization is based on the facts and circumstances. However, if 1 tax exempt organization has the power to remove a director or trustee and designate a replacement, then that organization controls the director. [Q 12:14.] I'd say that in your situation, where 4 individuals who are representatives of another organization have the power to remove and appoint the president, that president would be controlled by those 4 individuals, and arguably therefore indirectly controlled by the other organization. That would mean 5 out of 6 of the directors meet the "representatives of or controlled by" test. Because that's more than 80%, the two organizations would be under common control.
Except for one thing. The funeral home isn't a non-profit organization. Prop. Treas. Reg. 1.414(c)-5(b)'s mandatory aggregation rule applies to pairs of exempt organizations, not to a charity and a for-profit institution.
The proposed regulations do reference a situation where charity A owns more than 80% of for-profit company B; they note that those 2 organizations are under common control under existing law. [Q 12:9, example 2.] But that's not the case here.
The only provision of the proposed regulations that could be fairly said to potentially apply is 1.414(c)-5(f), which says that in abusive situations involving a tax-exempt and one or more other entities (of any type), the IRS can treat the 2 as being under common control. This is a pure "smell" test, and we don't know how the IRS will apply it. We can only hope that the National Office will use this tool as judiciously as it does similar "abuse catch-alls." [Q 12:17.]
Ultimately, if the proposed regulations are finalized in their current form, your two organizations might consider getting a formal ruling, to put the potential abusive situation issue to rest. But in the end, given the structure you've laid out, I don't think they need to be concerned about Prop. Treas. Reg. 1.414(c)-5(b).