You cannot make heavier elements from Iron only
First, you seem to be familiar with the binding energy curve for elements.
As you can see, iron is at the top of the binding energy curve, so it has the most energy per nucleon. If you wanted to 'fuse' iron into something heavier, then you need to add energy.
This is not impossible to imagine happening. The conditions inside a supernova allow nucleosynthesis of elements heavier than iron, so incredible though supernovas may be, perhaps some super-advanced alien race could accomplish it by adding enough energy to a giant iron core.
You need more neutrons
The problem here comes from the number of neutrons present in Iron. Iron does not have enough neutrons to form Uranium or some other heavier elements that you suggested. Having iron and only iron in your core gives you a limited number of things that you can make. You can only add nuclei together that have 26 protons in them, so the first order fusion products will all have 52 protons, and somewhere between 56 and 64 neutrons.
From a chart of nuclides, we can see that none of these configurations is stable. 52 protons is tellurium which requires at least 68 neutrons to be stable. Thus, these short term fusion products will decay, via $\beta+$ decay, into mostly tin, with some cadmium, indium and silver and the like mixed in, depending on the initial isotopes. This decay takes elements 'down' the periodic table; tellurium has a higher atomic number than any of its products, so $\beta+$ decaying isotopes will end up with a lower number of protons once the decay chain stops at a stable isotope.
This process could potentially continue, with the tin fusing with another iron atom to make osmium, which would decay into ytterbium or hafnium; that could then pick up another iron, etc. The problem is that eventually your fusion products are going to be elements large enough that they need massive amounts of neutrons to maintain stability. While iron can be stable at 14:13 neutrons:protons, lead is only stable at 62:41; and uranium's most long lived isotope is 73:46.
Ultimately, large atoms that are sufficiently neutron deficient will start to undergo $\alpha$ decay, where they lose an $\alpha$ particle which is 2 neutrons and 2 protons. In this decay, they will rapidly drop atomic number until you are back close to where you started.
To 'fuse' heavier elements, you need neutrons
Heavier elements obviously got created, but how? By the r-process, where nuclei of atoms with atomic numbers above iron accumulate extra neutrons. These extra neutrons cause isotopes to $\beta-$ decay. The result of this decay is that an element moves 'up' the periodic table, gaining atomic number as unstable neutrons turn into protons. This is the only way that mostly stable elements high up in the period table (like uranium and thorium) can be formed.
The r-process occurs in two situations (that we know about). The first is a neutron star collision, where there are obviously plenty of extra neutrons to spare. The second is in the core of a Type IIb supernova, the most violent kind. Much is unclear about how this works; there has only been one observed, nearby Type IIb supernova, and the first neutrons star merger was observed in 2017.
Here is a chart of the source of nucleosynthesis for elements.
You can see that the neutrons star merger (which is also possibly occurring in Type IIb supernovas) is how you get the vast majority of your heavy elements.
How can you get enough neutrons?
In a supernova, and in stars in general, neutrons form from the p-p fusion chain. Two protons fuse together, a highly unstable configuration. This immediately (as in, no measured half-life immediately) $\beta+$ decays into deuterium, which has a neutron. Deuterium can then fuse with other assorted combinations of hydrogen and helium to form free neutrons. In a core collapse supernova, the neutron flux is theorized to be such that extra neutrons can accumulate to the heavier elements, thereby making even heavier elements.
From your alien's perspective though, the best way to add neutrons has got to be a neutron star. If they can get their hands on a galaxy's worth of iron, they can probably find a neutron star lying around too.
How to fuse an iron ball into heavier elements
Take a giant iron ball, add an immense amount of energy, and then throw in a neutron star. Metal!