Your real questions are: 1) Are you doing a good job in the contracted company? 2) Will it be a disaster if you loose this job? If you are doing a good job, these kind of consulting firm will want to keep you as they do not want their client to be unhappy, not to mention that they earn lots of money from you anyway. Still, there is very small possibility (based on the assumption that you are doing a good job) that you could loose the job if you do not sign the new contract.
If "yes" to first question and "no" to second, if I were you, I would tell the consulting firm that you want to keep the original contract (unless they raise your hourly pay to get rid of holiday pay and etc). In any case, they could not take your 5/26 pay. (Small claim court might be able to get your pay back if they insist withholding the money; actually, a lawyer's letter might be enough to do the magic.)
Good luck! (And keep us posted, please.)