I have an alternate suggestion: can the older boys start to help with some of the slack? Once a week vacuuming and making dinner and doing a load of laundry from start to finish - it's their clothing too, right?

- won't break their backs.

That and making friends with a slow cooker for at least one meal a week (2 or 3 is good too

) have saved the sanity of lots of folks.
And then when DGS begins to work out of this phase (into some other thing like teething LOL), you'll have a nice foundation laid and you'll get to put up your feet once in a while. Ideally, anyway.
But seriously, this too shall pass. He may also be clingy if he's cutting teeth, and once they're in there'll be more..... (must stop now, having flashbacks. LOL)