have you passed the life in uk test ?

is your visa app straight forward - have you been with the same employer, if not is there any gaps btw your work permits, how many days have you been out of the uk

if you case is not straight forward, then i wouldn't use a PEO same day,, you might lose your money or they might not be able to do it same day

if it is straight forward, maybe a solicitor can get cancelled appointments but what if they can't you'll be waiting anyway and it will cost you more ..