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The home/road split question was for a time, partially addressed by the F/S Matrix.  One of the variables the matrix tested was how each team's offense and defense uniquely reacted to each park in which they played.  Solved for simultaneously with all of the other variables (offensive skill, defensive skill, strength of schedule, intrinsic park factor, umpire factors, league context), I got some rather interesting and suggestive results, mostly for "extreme" teams.  The 2001 Mariners, for example, reacted uniquely well to Safeco Field both offensively AND defensively (their net mark reaction scores were +0.326 R/G scored and -0.605 R/G allowed)...i.e. a lot of their success that year may have been attributable to their being ideally taylored to Safeco.
When I put starting pitchers into the matrix (to improve my understand of the strength of defense faced by each offense), the park reactions became highly unstable and caused everything to look way wrong.  We think that having too many small-sample variables in the matrix causes it to lose sight of the best solution.
The alternative approach, at least in the PBP era, will be to rate everything as normal but account for how defenses react to each park as a sort of side-calculation for further research.