I just completed the GDMBR on a hard tail fitted with Titec H-Bars. I also own a small Arkel handlebar bag. Your lucky day!

1) Room between front of H-Bar for a small Arkel bag: No. Not even close. I have XT M770 dual controls where both the derailleur and brake cables also would interfere. Wouldn't you also have a conflict with at least your brake cables?
2) Cutting the bar is inadvisable. There's barely enough room as it is for the fists using the bar's vaunted "aero" position.
3) Thumbies ought to work, but you'd want them where my dualies are mounted (something like this: http://www.jonesbikes.com/h-bar.html - half way down the page) and the cables would again interfere with your bag.

The H-Bar's "aero" position was helpful to stretch the back, but the other hand positions illustrated in the link above are too similar for them to offer much relief. A conventional MTB bar with bar ends allows a 90 degree rotation of the wrists and a moderate stretch of the back. I think I'd go instead with the latter and have a chance to mount a handlebar bag or better yet mount something like this http://www.revelatedesigns.com/index...=3&ProductID=4 and try to avoid a front rack and panniers.

I have Rhyno Lite rims, but the narrowest tire I'd care to mount on them is 35mm. I have Dyads on another bike and the narrowest I'd go on those is 28mm. I am not aware of a rim that will unquestionably take the range of widths of tires you want.