Hmm, in that case I would say it's completely up to the DM (which I'm assuming is you) whether a Forcecage type effect would block the "anti-magic/dead magic" areas and allow spellcasting...
There is already a magic item that puts up forcecage effects: Cube of Force
I would think it needs to be more on the epic and/or artifact level though to overcome anti-magic/dead magic since not even Mages Disjunction has the ability to 100% overcome an anti-magic spell and MD is 9th level...
If you could make a horizontal wall of force? Sure. But the spell descriptions explicitily states a "vertical wall of force"
Forcecage only has a 10' diameter so only 1-2 characters could fit in there.
Oh, and I don't think the force effects are moblie in any way... so that's another obstacle...
Not sure how much usefulness you would get out of this though... you would have no line of effect and so couldn't cast spells on anyone outside of your "magic-area" anyway.
But even if Wall of Force blocks Antimagic, there is one problem. How will you go inside the area encased by the Wall of Force? You cannot teleport into it as your magical abilities are suppressed. Also, you can't get out of that "force walled lab" as you cannot teleport out to dead magic area.
Planar Travel: As a mode of planar travel, a gate spell functions much like a plane shift spell, except that the gate opens precisely at the point you desire (a creation effect). Deities and other beings who rule a planar realm can prevent a gate from opening in their presence or personal demesnes if they so desire. Travelers need not join hands with you—anyone who chooses to step through the portal is transported. A gate cannot be opened to another point on the same plane; the spell works only for interplanar travel.