Galaxy formation theories predict that galaxy shapes and angular momenta have nonrandom alignments with the cosmic web. This leads to so-called intrinsic alignment between pairs of galaxies, which is important to quantify as a nuisance parameter for weak lensing. We study galaxy–cosmic web alignment in the IllustrisTNG suite of hydrodynamical simulations at redshifts 1 and 2, finding that alignment trends are consistent with previous studies. However, we find that the magnitude of the spin alignment signal is ∼2.4× weaker than seen in previous studies of the Horizon-AGN simulation, suggesting that this signal may have a significant dependence on subgrid physics. Based on IllustrisTNG, we then construct mock observational spectroscopic surveys that can probe shape–cosmic web alignment at z ∼ 1–2, modeled on the low-z galaxy redshift and IGM tomography surveys on the upcoming Subaru Prime Focus Spectrograph Galaxy Evolution (PFS GE) survey. However, even over box sizes of L = 205 h −1 Mpc, we find that global anisotropies induce a sample variance in the 2D projected alignment signal that depend on the projected direction; this induces significant errors in the observed alignment. We predict a 5.3σ detection of IllustrisTNG’s shape alignment signal at z ∼ 1 from Subaru PFS GE, although a detection would be challenging at z ∼ 2. However, a rough rescaling of the relative alignment signal strengths between the TNG and Horizon-AGN simulations suggests that PFS GE should be able to more easily constrain the latter’s stronger signal.