No, they can't. Congress isn't sovereign, but it isn't bound by any prior Congress. You could create an exception to parliamentary procedure for the agency, like we do for e.g. CBO, a legislative agency, but it wouldn't be able to actually do anything.
> the same manner that the current FTC does not need to ask for presidential approval
The FTC was created as an independent agency by the FTCA of 1914. A law passed by the Congress and signed by the President. It exercises Article II powers freely and limited Article I rule-making powers delegated to it by the Congress.
When the FTC takes executive action, it does so as an independent agency. When it invokes its rule-making authority, it's subject to all manner of checks and balances, from the President through the courts all the way to the Congress. Inverting that makes the agency useless. It would have rule-making authority similar to the Congress (i.e. subject to full passage and Presidential veto) but none of the executive powers.
I'll admit, this is one of the more creative ways of de-fanging an unpopular agency that I've seen. (I still can't tell if it's parody criticism of Chevron.)