I don't think gasoline is appropriate. It often contains very unhealthy additives. Many foams dissolve quite readily with acetone, especially styrofoam. However, acetone is very volitile and evaporates easily. Try MEK, methyl ethyl ketone (butanone). It is less volitile and is very similar to acetone with respect to dissolving foams. If it works you won't need much. A game that chemistry teachers play with styrofoam is to have students guess how many foam packing "peanuts" will dissolve in 50 mL of acetone. It holds more than 100! When the dissolved foam/MEK gets thick change to fresh solvent. MEK is cheap and available at Home Depot type stores.

And as to using benzene, NO! Carcinogenic. Seriously bad shite.
As to HCL, NO! It will eat the aluminum and is doubtful on the foam.
As to "caustic", poor choice of words. This often relates to bases or lye products, not ketone solvents. Otherwise it relates to eating living tissue and actone or MEK won't do this either.

P.S. Don't confuse MEK with MEK peroxide catalyst used with epoxy resins.