So you have the private keys for that address?
If so, surely you can just import the private keys into a wallet that lets you specify fees manually... then you can just create your own transaction (with whatever fee you want) that will consolidate the funds into another address...
WARNING: looking at the history of that account and what the others have calculated... the data size of the transaction to consolidate all those inputs will be HUGE. It seems you have something like 200 inputs to that address all at 0.001 BTC???
Anyway, if you go for the 120 sat/byte "recommended" fee, it is going to get quite costly... you can always choose something smaller and hope for the best... pick a time when the mempool is not flooded with transactions, say less than 10K unconfirmed transactions... and then I would even suggest making sure your transaction has at least a 0.0001BTC/KB fee (that's only about 10 sat/byte) and then using the ViaBTC Transaction Accelerator (
https://www.viabtc.com/tools/txaccelerator/) to try and get your transaction pushed through...
Looking to the future, is there anyway you can get these transactions bundled together? I assume it is an automatic payment from some activity... can you set the payment threshold to something higher, so you get say 10x 0.01 BTC payments instead of 100x 0.001 BTC transactions?