Yes indeed, you can do that, if the genes have been "stabilized" some people don't like that term, the result should be the same, you should have relative uniformity. The caveat being I am not sure how age effects the seeds vigor. There are many ways you could go about this.
If we are only looking for the signs of a Homozygous gene pool you will want to run a couple generations at the very least.
If you just want to have some really good bud, You could take clones, let the originals grow out see which ones are the most desirable, choose your candidates reverse the females and pollinate each candidate with it's own pollen.
The issue with my original statement is if they are not homozygous you will have gone down the genetic rabbit hole another generation, which means you are getting further away from where Renee originally was. It all depends on how you want to go about it, if you are more concerned with good bud, do what you mentioned, if you are concerned with preservation it will take patients and perseverance and a bit more research to find out the lineage etc.
Either way it is a very worthy journey and one that will teach you a lot.
Hope all works out for you Brother :)