We have taken the position that with new ownership, you should not confuse the previous company history with the new. (CTR exemptions come to mind.)
Close the old accounts and open new ones with new due diligence, the whole nine yards. You'll be better off in the long run. You might offer them some services, checks, etc. to offset their inconvenience, but I would stand firm.
We had a similar instance and it caused a lot of pain and confusion on the part of the bank to allow the new company to use the existing accounts.
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"No problem can withstand the assault of sustained thinking." ~ Voltaire
"Sustained thinking gives me a headache." ~Me