We really don't need yet another license. What's more, all those changes would probably result in a new license that is again incompatible with GPLv2. The fact is that the "anti-tivoization" clause is, for most free software projects, a smaller problem (if a problem at all) compared to the simple fact that the GPLv3 is incompatible with the GPLv2. I fear there is simply no way of creating a "new" GPL license that is compatible with the GPLv2, short of adding an exception like MPLv2 does.

You could, but you could not change the license of code licensed as “GPLv2 or later”, since the full phrase is “under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.”. So only a “GPL” published by the FSF would count as a “later” version.

Seems easier to license your software under GPLv3, along with a statement that you waive licencees form any obligations placed upon them by the clauses you don't like.

If I remember correctly, GPL itself is copyright FSF. I don't think you can use it as a base for derivative work.

Besides, why would you want to go back to v2?! I found no strong argument for v2 except for supporting tivoization.