Hi Jon,
What to do will reflect the uniqueness of your site. This is hard to assess without being there. But I will take a stab at it with a post because it makes my heart sad to see the consideration of herbicides. This too, is likely to be just a short-term "fix".
I just finished reading the book
Beyond The War On Invasive Species by Tao Orion. I found the perspectives it presented quite interesting, if not compelling and it expanded my thinking towards plants that pose a challenege in the landscape. At the end of the book the author briefly outlined a series of actions for implementing a management plan based on
permaculture. I recommend the book to anyone interested.
I'll summarize some thoughts real quickly using the lense of this book.
Take advantage of the successional tendencies of nature. Landscapes are evolving through a series of stages with different plants serving different functions. The dog fennel may be filling a niche or a void that is present in the current state of successsion for your environment. Explore the "benefits" this plant is fulfilling in your landscape. Then look at additional ways to replace it with more useful plants that do the same thing. The plowing and planting of grass is on the right track in this regard, but I'm thinking in terms of more diversity.
The only suggestions i can come up with right now is mow the fennel before it goes to seed. Harvest the biomass and use it for mulch or
compost. Plant something that would appear in the next stage of succession like shubs and
trees to compete with the fennel and eventually shade it out. Harvest the lumber. Reseed with a pasture mix and return grazing to the area.
The solution is likely to include multiple strategies. I hope other creative ideas get posted.