As for the dust inputs I don't think you could ever use those. I have one address that contains dust from the 2015 spam attack and I cannot spend it. It totals to 1.86 btc, all made up of dust inputs.
Out of curiosity... could you share this address with all those dust? Are you certain they cannot be somehow consolidated? I won't assume to know more than you but there seems to be one way at least to try do this.
I wasn't aware there was this much lying around (only came to the scene last year. I sent you a PM in case you don't want to share. I have a few ideas!
I'm gonna sift through my files from 2015-2016 just to find that wallet. I'm willing to share the said address and also try to spend the inputs (again) but most probably the client won't let me since it requires fees more than the 1.86 btc total sum (individual inputs were at 0.0001 btc each).
Can't you configure mining software and hardware to look for your transaction specifically on the block chain and send all the dust to another address with 0 transaction fee to avoid the dust never being confirmed .
Mine it yourself .
Someone like macbook-air might do that for you for a discounted rate. It is a bit of a bad thing to do.
What size is the transaction, I'll see if I can calculate the minimal fee for it?