This is something others with pending orders should take note of. Take screenshots of the product pages asap, it's very likely you will need them if you do a chargeback.
If the current product page shows a delivery date that is further in the future than what it said when you placed your order use a website such as the Wayback Machine to try and get a screenshot of the page as it appeared on/near the date you made your purchase.
If TBI changes the ETA on the product page, that new date falls outside of your chargeback window, and you don't have proof that this wasnt the original delivery date, you may lose any chance to get your money back.
The banks tend to require proof that the item is overdue before they can start chargeback procedures.
From prior dealings with banks they told me you shouldn't cancel a chargeback until you either have the item or your money as they cannot reopen a dispute once it's closed, so keep that in mind.
In the past certain stores have responded to a chargeback by sending the customer or the bank an email claiming the item is on its way, specifically to get the customer to cancel the dispute, but once you do that if they don't send the item you have no action left other than going to court.
By deadline do you mean TBI's deadline to respond to the disputes, delivery dates that need to pass, or something else?
Not sure if this is applicable in your case but it might be worth trying, you could send a screenshot to the banks showing that the response to the chargeback was to cancel all orders without refunding.
If they are still waiting for a response from TBI it may may speed up processing for any pending disputes, and it should allow you to start disputes on any items whose delivery dates haven't passed yet.
Chargebacks can take a while depending on a few circumstances. It took about 3 months for my disputes with PC to be settled (mainly because that guy lied to the banks about a lot of stuff which caused delays) but some people had their money back within a month, so your mileage may vary.
You can also leave feedback on ProductReview (Click here) for further exposure if you want to continue to warn and inform.
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PS: Apologies for the wall of text, I think I may have posted a lot of this information in the past in another thread, but that thread no longer seems to be available to the public so it's worth repeating for new members.