Yes, you can. I'm not a tax specialist but I send a monthly payment to the IRS for my business.
I've found it has a few benefits:
You write smaller checks vs. paying all at once
You can better understand your business's true profitability
You can make adjustments to your monthly payments if you expect a divergence from your sales estimates
The term for this is a Chain Marriage. Google results for examples are filled with hits for the phrase "ball and chain", but I did find one example that lasted 117 years.
As far as I know, these are not considered the same estate by the IRS, so there would be no presumption of fraud.
Yes, its all about the paperwork.
But realize that Form 5310 is filled out by the plan sponsor who is your now gone employer. Your 401k provider is only following instructions of whomever is control of the remains.
Do remember that in the US the 401k as a retirement plan was accidental construct of the tax code. Legally the now defunct company is only on ...