What could a lay follower do to increase his zeal to become a monk?
I could easily have written your query. At this time however there are a few differences which may be helpful if shared. 

Am in my mid 40’s. Never thought that it was actually possible. Met a Venerable at the local Vihara who stated otherwise and has taken me under his wing so to speak with ordination to be the outcome. Yes, it’s a long road, lots to learn. But if it’s truly in your heart, it will be. Make yourself visible and learn as much as you can from as many as are willing to share. Have you decided upon a school of thought? So much to consider.

Please forgive for giving what equates to being advice, but the same is also my personal experience. Hope this is helpful in some small way.

All the best to you.