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With the rapid advance of wide-field surveys it is increasingly important toperform combined cosmological probe analyses. We present a new pipeline forsimulation-based multi-probe analyses, which combines tomographic large-scalestructure (LSS) probes (weak lensing and galaxy clustering) with cosmicmicrowave background (CMB) primary and lensing data. These are combined at the$C_\ell$-level, yielding 12 distinct auto- and cross-correlations. The pipelineis based on $\texttt{UFalconv2}$, a framework to generate fast, self-consistentmap-level realizations of cosmological probes from input lightcones, which isapplied to the $\texttt{CosmoGridV1}$ N-body simulation suite. It includes anon-Gaussian simulation-based covariance for the LSS tracers, several datacompression schemes, and a neural network emulator for accelerated theoreticalpredictions. We validate our framework, apply it to a simulated $12\times2$pttomographic analysis of KiDS, BOSS, and $\textit{Planck}$, and forecastconstraints for a $\Lambda$CDM model with a variable neutrino mass. We findthat, while the neutrino mass constraints are driven by the CMB data, theaddition of LSS data helps to break degeneracies and improves the constraint byup to 35%. For a fiducial $M_\nu=0.15\mathrm{eV}$, a full combination of theabove CMB+LSS data would enable a $3\sigma$ constraint on the neutrino mass. Weexplore data compression schemes and find that MOPED outperforms PCA. We alsostudy the impact of an internal lensing tension in the CMB data, parametrizedby $A_L$, on the neutrino mass constraint, finding that the addition of LSS toCMB data including all cross-correlations is able to mitigate the impact ofthis systematic. $\texttt{UFalconv2}$ and a MOPED compressed $\textit{Planck}$CMB primary + CMB lensing likelihood are made publicly available. [abridged]

$\mathbf{12\times2}$pt combined probes: pipeline, neutrino mass, and data compression