Not on either schematic you've posted thus far!I already had a transistor hooked up i the same configuration on the original schematic.
Look, if you want to get some decent insight into why things aren't working, you're going to need to take the time to draw up a proper and complete schematic with all of the parts you're using. The more complete and accurate your schematic is, the better our help will be.
The less information in the schematic, the worse our guessing will get.
If you posted a complete and accurate schematic, we could run simulations on it to figure out where things were going wrong.
As it is, the 555 timer will be running at a very low speed, and current decay in the primary will be slow because you are not snubbing it, except for the Vf of the diodes and the resistance of the primary winding. If the diodes in the primary start to get warm, their Vf will drop, which will decrease their snubbing effect, which will hasten the onset of core saturation.
You'll wind up with an ever-increasing DC current flow through the primary as the diodes heat up, right up until the MOSFETs can't handle the current anymore. Disaster will strike quite suddenly.