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I do re-project my "raster" maps using a complex process involving a free graphics manipulation program: imagemagick.
The vast majority of the maps I make are Garmin Custom Maps - and for some reason most of the maps I download (USGS topo, park maps available online) are in a different projection such that things are terribly askew with the Garmin Custom Maps.  Fortunately, they have some guide marks on them (16 of them for the USGS topo maps) that show where the LAT/LON are supposed to be.
There is a manual process by which I find these hash marks and use imagemagick to force them into a proper grid.  Imagemagick takes my measurements and shifts every pixel on the map according to a 5th order polynomial in order to minimize distortions across the entire map.  After I use this process, I then put the shading in (which, for some reason, is provided in the proper projection).  I wrote a script to simplify this process.

I'm sure there is an easier way with something like GRASS GIS, but my chosen method seemed the path of least resistance with what knowledge I already had.

Boyd - I definitely agree that there are limitations with the Custom Maps as implemented by Garmin.  There are ways around that limitation, but in general covering the area of a state with such maps is entirely impractical.
However, it is not difficult to generate very nicely detailed maps (much more detailed than what Birdseye offers) for a reasonably large area like Big Bend, and, prior to taking a trip to Big Bend, loading up the maps on the Garmin.  So, my intent is to generate maps to places I would like to visit, and load the maps specific to that region prior to leaving on the trip.
Its also possible to carry several memory cards and swap them out in the extremely unlikely event that a single trip would involve more maps then could fit on a single memory card and/or exceed Garmin's entirely unnecessary limitations.

Anyway, I have a procedure nailed down and have thoroughly enjoyed the learning process.  I'm happy to share the fruits of my labor if anyone else would find it useful.

Sorry if this is a dupe - I made an account specifically to respond to this post and the reply isn't showing up.
Norm - I have created a process to convert USTopo maps to .jpg images, and a seperate process to create some nice custom shading that looks much better than the shading they provide on the Topo maps.
I'd be happy to share the process with you if you are interested.  As Boyd mentions, it isn't exactly trivial, but it uses all publicly available maps and open source software.
I'm attaching a small example - if you have GoogleEarth or some other way to view .kmz files you should see a small shaded topo map in the Big Bend area of Texas.