Wouldn't multiple address transfers collect individual fees making the transaction still super expensive ? If I understood correctly he wants to use multiple wallets with little amount of BTC in them. I would say to hold the funds until the txn fee issues are solved
The key is that you send all the dust in one transaction with a very low fee to a single address (preferably a segwit address). The transaction will take a long time to confirm, so you must plan ahead.
As for waiting "until the txn fee issues are solved", I don't expect that to ever happen.
Indeed, or ask someone in this forum to accelerate your transaction, there's currently dozens of threads out there, here, https://bitcointalk.org/index.php?board=52.0. I'm not sure how many of them are simply baiting for donations/posts,, but by the looks of it it seems that some of them actually are working.. Worth a try aslong as they are out there, right?
Alternatively you can do it yourself as i stated in one of my previous posts by using https://pool.viabtc.com/tools/txaccelerator/, although this accelerator is usually full after a few seconds.
You can try to add your transaction again every hour.