Rob,
I don't know the size of your machine, but on our Case 580K (good sized backhoe), we move with the hoe quite often.
Some advice if you do so.
1. Leave the parking brake ON. If you have to reposition your hoe to get another bite, the tractor won't roll backwards. Also, if you have to move the hoe in a hurry for stability, the tractor will stay where you put it /forums/images/graemlins/smirk.gif
2. Obviously, lift the back wheels off the ground with the hoe. We normally have them lifted by the stabjacks anyway, so just drop the hoe, raise the stabilizers. The wheels should only be about 2 inches off the ground. There are some serious stability issues, and you wouldn't want to invite a tip.
3. When digging, always have the front bucket on the ground with at least slight down pressure, but don't lift the front wheels completely (unless using to level for dig). Don't forget to lift the front bucket before pushing. Again only a few inches, for the same stability reason.
4. Using the hoe...Small steps are better. Straighten the bucket all the way or close, raise it above soil and use your extension arm (the cylinder between your main lift and your bucket right in the middle of the hoe) to position your hoe about no less than halfway extended. Let me say this another way. If your hoe is in an upright "A" shape, then move the extension arm to place the bucket and extension arm just a bit further extended than straight below the end of the extension cylinder at the tip of the "A". Extend it just a bit more to be sure.
IMPORTANT: If your hoe bucket is closer to the tractor than directly beneath the top end of the extension cylinder, the position will be extremely UNSTABLE when lifting the stabilizers. (We've done it, but you have almost NO CONTROL over left/right tilt of the tractor) Extended beyond this point gives some left/right stability and control.
5. When moving, extend the arm some, then lower the hoe as necessary to keep the wheels about 2"-3" off the ground. You can reposition the hoe as many times as you like. If you try to move t0o far, most people have problems with the arc of the swing, then have to play too much with up/down.
If pulling the tractor back, don't retract the arm beyond the center point mentioned above.
HINT: When backing into a dig spot, it may help if you extend the hoe about 3/4 of your reach for your working reach/depth, about 3"-4" off the ground and *gently* back the tractor until the hoe is where you want it. Watch the hoe doesn't contact the ground or go too high. This is also low stability, but usually okay if on level, flat ground and helps reduce the need for repositioning.
Good luck, and be careful.
-JC
PS- Forgot the disclaimer: Always follow the instructions in your manual and never operate your equipment in a manner contrary to what is recommended therein or in a manner not recommeded therein. The above is what "I" do and how it can theoretically be done, and is not in any way a recommendation or inducement for anyone to attempt to repeat or reproduce said acts... etc, etc, etc.