Any chance that amended returns simply put in for the unemployment issue are being processed faster than 16 weeks

The iRS does not want you to amend for the unemployment tax law change, since they are taking care of it without the need for you to amend-----and they are already clogged with too many amended returns.   Did you already amend anyway?

Even during “normal” times it takes about four months for the IRS to process an amended return.  During the pandemic and due to the severe backlog at the IRS it is taking much longer—six months or more for many amended returns.  Do not expect quick results from amending.  When the IRS issues a refund for an amended return it will be by check.  They do not make direct deposits for refunds for amended returns.  You can watch for information here:

https://www.irs.gov/Filing/Individuals/Amended-Returns-(Form-1040-X)/Wheres-My-Amended-Return-1

The IRS began to send out the additional refund checks for tax withheld from unemployment in May.  The refunds are being sent out in batches—starting with the simplest returns first.   If you are eligible for the extra refund for federal tax that was withheld from your unemployment the IRS will be sending you an additional refund sometime during the next several months.  TurboTax cannot track or predict when it will be sent.  The IRS has not provided a way for you to track it, so all you can do is wait for the refund to arrive.

https://ttlc.intuit.com/community/tax-topics/help/how-do-i-get-the-new-unemployment-benefits-if-i-ve-already-filed-my-taxes/00/2081053

Please read this very recent news from the IRS:

https://www.irs.gov/newsroom/irs-to-recalculate-taxes-on-unemployment-benefits-refunds-to-start-in-may

https://www.irs.gov/newsroom/irs-begins-correcting-tax-returns-for-unemployment-compensation-income-exclusion-periodic-payments-to-be-made-may-through-summer

https://ttlc.intuit.com/community/tax-credits-and-deductions/help/am-i-eligible-for-a-new-credit-or-deduction-because-of-the-unemployment-income-exclusion/01/2211778

https://www.irs.gov/newsroom/2020-unemployment-compensation-exclusion-faqs

https://www.irs.gov/faqs/irs-procedures/forms-publications/new-exclusion-of-up-to-10200-of-unemployment-compensation

filing an amended return could actually delay your refund. amended returns are in some cases taking up to 6 months.