Can I combine two separate 120V isolation transformers, tie the secondaries in series, but not tie the primaries?
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Three options - two of which actually work. Note the dot convention on the coils.


(a) is the same as your schematic (but lower primary is inverted to keep phase convention the same). The primaries are in anti-phase so the output is zero (as pointed out in the comments).
(b) is the corrected version of (a).
(c) is an alternate working solution. Since the primary currents are the same what comes out the bottom of XFMR3 must go in the top of XFMR4 so there is no neutral current and the neutral connections can be omitted as shown on XFMRs 5 and 6.