  Berry phase interference arguments that underlie the theory of deconfined
quantum criticality (DQC) for spin-$\frac{1}{2}$ antiferromagnets have also
been invoked to allow for continuous transitions in spin-1 magnets including a
N\'eel to (columnar) valence bond solid (cVBS) transition. We provide a
microscopic model realization of this transition on the square lattice
consisting of Heisenberg exchange ($J_H$) and biquadratic exchange ($J_B$) that
favor a N\'eel phase, and a designed $Q$-term ($Q_B$) interaction which favors
a cVBS through large-scale quantum Monte Carlo (QMC) simulations. For $J_H=0$,
this model is equivalent to the $SU(3)$ $JQ$ model with a N\'eel-cVBS
transition that has been argued to be DQC through QMC. Upon turning on $J_H$
which brings down the symmetry to $SU(2)$, we find multiple signatures -- a
single critical point, high quality collapse of correlation ratios and order
parameters, "$U(1)$-symmetric" cVBS histograms and lack of double-peak in order
parameter histograms for largest sizes studied near the critical point -- that
are highly suggestive of a continuous transition scenario. However, Binder
analysis finds negative dips that grow sub-extensively that we interpret as
these transitions rather being pseudocritical. This along with recent results
on spin-$\frac{1}{2}$ models suggests that deconfined pseudocriticality is the
more generic scenario.
