To TS I think u should taken the job and have the contract include a clause that says to some extent your salary will be reassess after x months of work or better still morale by 20%. I think if they serious about hiring u they would consider. Btw u are the final shortlisted??
Can share how much is 20% in your case per month? Just to gauge if haggling over it is worth it.
U should also consider the prospect this new co offers versus your current job. Sometimes money may not be everything.