I'm not inherently against crossovers but Marvel, LotR, and DW are terrible candidates just from their different rules alone. LotR is past centered, has medieval technology at best, magic is so rare it's almost non-existent, and other races are as populous as humans and live with them on the same planet. Marvel is present centered, has futuristic technology, magic is huge and game-breaking (seriously Doctor Strange could take on all the non-magical avengers at once and win), and humans dominate the planet with other races living only where humans cannot (Atlanteans, Moloids, etc.) DW is future centered, has far more advanced technology than even the most advanced race in Marvel, magic is just another form of science, and aliens walk amongst humans mostly in secret. LotR has a subtle guiding hand theology, Marvel has active and interfering gods and godlike entities, and DW has no god with the Doctor acting as a guiding hand instead. DW is all about technical pacifism with the solutions always being brains over violence. Marvel and LotR prefer combat with heroes.
Then there's the power creep issue. Like Archie meets the Punisher, crossovers get ridiculous when one side is clearly stronger than the other. The aforementioned story played it for laughs and it only lasted a single issue. Doctor Strange would kick Gandalf's ass without a second thought. Thor would wipe the floor with Aragorn. Anyone should technically beat the Doctor because he isn't a fighter but, chances are, he'd pull some trick out of his ass and defeat everyone up to and including the One-Above-All. No matter what, someone looks like a chump.
Maybe just crossing one over with the other. Definitely not all three. I also really don't think LotR would work with either of them. So Marvel/DW is theoretically possible but still highly unlikely. Even DW doesn't like alternate universes and the present shown on DW isn't anything like Marvel's.
Question though. By "reimagined canon characters," does that mean like an alternative universe? Like the ultimate universe? 'Cause I like that idea. Means less continuity to worry about.