I have tried viabtc to accelerate my transactions but all the times I got error message of over flow or something similar to that. Do we need to watch and wait till they will mine a block so that they will start accepting new transactions to accelerate to be included in their next block to be mined by them.

I do see almost all the people got chances to find this services more useful to them, but unfortunately I have tried with them when they could not accept no more transactions for their next push.