It's a little more complicated than that but, yes, she can get to that point under Keltham's onerous conditions without spending too much time. Two fucking Ioun Stones orbiting your head commands a lot of commercial respect. A devil-wrought lesser artifact is something you get by being on sufficiently good terms with Hell; Ioun Stones take money.
The interior of the building is over-warm by Golarion standards and very temperate by Elemental Fire standards, replete with air she could breathe without even a Planar Adaptation. There are mortal slaves here, drawn from the Material, who require more favorable living conditions. Though Carissa was only permitted to see a single chamber of slaves drawn from Golarion and the other planets of its star-system, for some reason or other; still, she could have had a Shobhad slave-warrior of Akiton, or a pliant and broken Lashunta of Castrovel, did she wish to piss off Keltham by buying such a person and then, presumably, mistreating them.
Mentioning that she wants to engage in secret negotiations with the noble Efreet owners will garner some looks even more arrogant than usual; and the Malik brought forth won't, in this case, agree to secrecy only on the basis of intended purchase. But statement of intended purchase, and 'token' payment of something worth around 2000gp, will do.
A sixth Wish diamond is sufficient to pay for the casting of five Wishes, even under the condition that the Malik must state and swear to its use: One of their number will hoard it through ages until he has assembled enough diamonds to raise the final abilitystat he requires to ascend into the next rank of Efreet nobility.
She will eventually end up in a windowless inner chamber of this place, as fiery as the rest of the interior was temperate, orange flames replaced by white flames shot with blue; hot enough that Carissa will feel it through the Planar Adaptation.