I would cover the hole with
Eternabond tape and then coat the roof with RV Liquid Roof material.
You can see how I did mine, including pictures,
here. . Please read that thread through to the last page for updates to my situation. My trailers roof should be very similar to what you have as my trailer is just about the same age.
The rv roof you mentioned would be fine also but much more expensive. To do mine was in the neighborhood of $3500. I had an appointment with
RV Flex Armor to get it done several years ago but cancelled it because of other problems. I suspect that the
RV Armor will be similarly priced.
Although a 15 years old rubber roof has lasted a long time, and has not leaked a drop during that time, it is nearing the end of its' normal life and could use some help. At least that is how I looked at it. :)
Barney