I applaud the effort by anyone to try and improve on a situation of unacceptablity; and I really would be interested in if this girdle provided accurately observed results, and exactly what, but believing the intention is to aid in the prevention of the two forward bearings from moving away from one another although it may render some assistance I question the effectiveness.
In transmissions that I have observed with displacement of these bore centerlines it generally displays the greatest sum of case material movement closest to the bearing races with a dissipation of material movement as one observes further from this area. I question if just clamping the outside surfaces really solves this? But if case fracturing in the horizontal plane, then well perhaps the idea is "good", but in that instance it would seem one might need something bit more substantial to offset this level destruction?
And don't over-tighten if applying an effective compressive force or one may note bearing/race failure as the bearing bore might be misshapen (made not round); perhaps a test of the bare case and measurement of any possible effect might be in order.
I have in the past, welded up damaged cases including adding material filling in the waisted areas between the webbing in an attempt to aid in the field, but I'm not going to say it may only prove to be "feel-good" effort, but one wasn't out anything as these were cases needing repair anyway.
On the third-gear tooth breakage issue, try and maintain a slight preload on the main and input shaft bearing sets front to rear (remember the case is going to grow in length with temperature), as this aids in reducing the deflection at the juncture of the input and main/output shafts, this reducing the tooth-climbing in the relationship and the resultant reduction in load carrying capacity of particularly the third gear set.
Scott.