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The strong force however has limited
range and when nuclei reach about the size of U the strong force
can no longer attract the particles with enough force to overcome
electromagnetic repulsion therefor such large nuclei do not last
long.
This explanation is incorrect, or at least, incomplete. Think of
a chain of students holding hands. The force is short range - two arm
lengths - but there is no limit to the length of a possible chain.
You are correct in pointing to competition between the coulomb
force (proportional to Z^2) and the nuclear force (proportional to A)
as limiting the number of protons. This leads to the existence of a
proton "drip line". There is also a neutron "drip line" - possibly
because of the Pauli principle limiting the number of neutrons that
can be near the center. So having the right mix of n and p is crucial.