Did the trustee not want it processed? Does the "TPA" also hold the plan assets? If not, how did the money get paid out by the recordkeeper/custodian? Is the TPA an authorized signer on the account? If so presumably the trustee approved this? If not, it shouldn't have been processed by the RK. Why did that happen? Too many unknowns to opine. Assuming TPA isn't engaged to do this, they need to tighten up procedures to prevent it from happening again and TPA should not allow itself to be an authorized signer on the account.
You got me thinking and I found this PLR. I think it says the IRA left to estate can be rolled by surviving spouse to IRA. No income tax due. Anybody got time to check it out? Its only 4 pages.
Thanks
IRS PLR 201931006 IRA Payable to Estate can be rolled over by surviving spouse to new IRA.pdf
Code 3H is how you indicate a controlled group, similar to how you put 2J for the 401(k) arrangement. And a controlled group is still a single-employer plan, indeed.
You may want both of your entities to adopt the plan, though, if they haven't already. Fidelity should have a supplemental page to list adopting employers. I suppose it's your choice which you wish to have be the primary.