Much easier than compiling Wine and maintaining the modified Wine version ;) I did it and it worked for Outlaws!! Here is an example:
https://gist.github.com/shmerl/baa5367fce111e6999a4

Similar hack can work for other GOG games which use ogg-winmm. Just use grep to detect all usage of the DLL.

I hope Wine developers will fix it though, so there won't be a need for such hacks.

Hmm...I've tried WINE 1.7.39 in Wineskin under OS X 10.10.2 (and PaulTheTall's Porting Kit, which apparently uses a CX 13.2.0 WINE engine?), and in both cases, the game sputters and dies when I try reconfigure my keyboard...which sucks as I'm a leftie and don't use WASD. The game works great in full screen using nGlide, though.

Edit: There seems to be a problem with keyboard input; I type in keys and gibberish seems to come out when I try to name my savegame files. I wonder if this is related somehow to the problem I've had with rebinding keys. I've tried PortingKit, Wineskin, and CrossOver and nothing seems to work.

Latest Wine is broken with Outlaws. See this bug: https://bugs.winehq.org/show_bug.cgi?id=35718

Try Wine 1.7.12. I have that keyboard problem too. The numeric keypad works though. So I just name saves as sequential numbers.

Another annoying bug - Outlaws keeps crashing once in a while in random locations. Did you notice it?

Just to clarify, Outlaws runs just fine under nGlide at full 1366 x 768 resolution with all of the gfx settings enabled on Wineskin with WINE 1.7.39. Otherwise, I've seen the graphical flickering/corruption on D3D mode with pretty much all WINE versions in 1.7.x. The game launches to a white screen on anything lower. I haven't yet encountered any random crashes, either in Wineskin or in CrossOver.

Using a dll override in winecfg for winmm (native, builtin) causes a crash, as you mention on the WINE AppDB, but it works in CrossOver.

And speaking of CrossOver, the game also runs fine, and with the music working perfectly well with the winmm override mentioned above. The only consistent problem is that keyboard input is bugged out when saving games, and I can't configure my controls at all.

How do you use nGlide? I'm not familiar with it. Game settings have two options D3D (which gives resolutions up to 1600x1200) and 3dfx which gives up to 800x600 I think. I was using D3D, since 3dfx doesn't work at all for me.

Yes, because CrossOver build Wine with delayed loading of some DLLs. Using the hack posted above this can be avoided in regular Wine.

That's not Wine specific and bugged this game for a long time even on Windows *saves). Not sure about the controller - I never tested it.

I figured out the crash. I didn't patch all needed binaries with winmm fix.
Here is the updated script (no crashes now so far): https://gist.github.com/shmerl/baa5367fce111e6999a4

OK, I figured it out. I run nglide_config.exe and set resolution to 1600x1200. It works pretty well and the game is more stable than with D3D option. Thanks for the nglide hint!

Is there any way to prevent resolution changing when going to the menu? That's where various crashes still happen.

So far, the most reliable mode for me with minimum problems is 1024x768 (with nglide).