Your only feasible options are Tier 4 materia and Allagan coins. You can spread out which kind of materia you buy, just try to stick with types that will translate to a gain rather than a loss once you get to your new home. This will allow you to sell off your stock faster since you will be selling in multiple markets rather than flooding a single one or a few.

The allagan peaces have the benefit of translating back to gil as soon as you talk to an NPC, the drawback being you will take time to gather them from the AH and at a guaranteed loss due to taxes and markup over their actual value by the seller.

Between the two I'd favor materia, if nothing else because the Allagan peaces outright introduce gil to your destination server while the materia just transfers others gil to you. SE might take a dim view of sidestepping their restrictions in this manner.