  Recently, we proposed that the one-loop tadpole diagram in perturbative
non-supersymmetric heterotic string vacua that contain an anomalous $U(1)$
symmetry, leads to an analog of the Fayet-Iliopoulos $D$-term in
$\mathcal{N}=1$ supersymmetric models, and may uplift the vacuum energy from
negative to positive value. In this paper, we extend this analysis to new types
of vacua, including those with Stringy Scherk-Schwarz (SSS) spontaneous
supersymmetry breaking versus those with explicit breaking. We develop a
criteria that facilitates the extraction of vacua with Scherk-Schwarz breaking.
We develop systematic tools to analyse the T-duality property of some of the
vacua and demonstrate them in several examples. The extraction of the anomalous
$U(1)$ $D$-terms is obtained in two ways. The first utilises the calculation of
the $U(1)$-charges from the partition function, whereas the second utilises the
free fermionic classification methodology to classify large spaces of vacua and
analyse the properties of the massless spectrum. The systematic classification
method also ensures that the models are free from physical tachyons. We provide
a systematic tool to relate the free fermionic basis vectors and one-loop
Generalised GSO phases that define the string models, to the one-loop partition
function in the orbifold representation. We argue that a $D$-term uplift, while
rare, is possible for both the SSS class of models, as well as in those with
explicit breaking. We discuss the steps needed to further develop the arguments
presented here.
