That is a very smart plan... avoiding small payments is the best move going forward...
To fix your current issue, you can always try a "consolidation transaction"... send ALL your coins to one address in a single transaction to create a single large UTXO... make sure the transaction fee is set to at least 10 sats/byte (10000 sats/KB, 0.0001 btc/kB) to meet their minimum fee requirements and then try and get it accelerated via the ViaBTC TX Accelerator.
I'd be tempted to go a bit larger and aim for 50 or 100 sats/byte just so you have some wiggle room if you calculate wrong.
PROS: Turns all your dust into one big UTXO so future transactions will be smaller size = less fees.
CONS:
Risky - if you mess up the fee calculation and it ends up too small and you can't use the ViaBTC TX Accelerator your coins could get stuck for a number of days...
Frustrating - you have to stalk the accelerator to try and get your tx submitted because the accelerator is always so full...
Slow - You have to wait for ViaBTC to then mine a block once it is submitted successfully.