For starters, what was the original battery, how long did it last etc., and why if it worked can't you use the same system.
Putting batteries in parallel is OK, but they need to be the same type, and it is best to put them both in fully charged so they both contribute to double the ampere hours capacity. If you put a fully charged battery directly across a discharged one you will loose some capacity However, if they have the same charged capacity, it would work since you only need another 6 hours. That being said, if the discharged battery becomes faulty through continued deep discharges, it could over heat and cause some damage eventually, common practice would be to electrically isolate the discharged battery from the fully charged one.
To get your 3V, If you are using something like a series string of Ni-MHi cells, you really do need to electrically isolate the discharged batteries. My feeling is that if you can bump up the battery capacity of the existing setup by 30%, that would be the tidiest way to go about it, it should then run for the full 24 hours.
Cheers,
Richard