Brian, I don't know how to say this nicely but it's a good thing your welder didn't try any harder or he really could have screwed this up more. It's not to late. This can be repaired. I suggest taking it not to a welding shop but to a machine shop where they do machine repair. They will understand how important it is to maintain the correct shrink fit and also keep the correct tooth pitch through the weld section. There are many ways to do this repair and each will use his own. The following is a way I may have done it.
First thoroughly clean the flywheel and ring gear, V out the repair area to remove the bad weld and stressed metal and make room for the filler metal.
Get a pitch reference 180° from the break by clamping two 1/4" dowels to the gear teeth about 4" apart. This will be used to set the pitch in the weld area. It might measure something like 4.1234".
On a CNC miller make a gauge block about 3" long with the inside gear radius on the outside and the outside radius on the inside. This will be used to locate and secure the gear while welding and to ensure all excess weld is removed from the inside.
With one clamp clamp the gear on the right side to a FLAT plate. Clamp the gauge block to the right side gear. Clamp the two reference dowels to the gear. Set the spacing to the reference and clamp the left gear to the plate and to the block.
Tack weld the root of the V with MG 600 TIG wire or equivalent.
With the block still attached remove the ring gear from the plate and finish welding the V. Grind off and excess weld. Put Prussian blue on the inside radius of the gauge block and rub it through the weld area. remove any high spots of excess weld that show blue.
There is probably about a .013" interference fit between the two components. Heating the ring gear to 400°F, 325° change, will increase its diameter about .037" so it should fall on the flywheel with .024" of clearance.