What kind of peas/beans is in max attract ? The picture on the tecomate site looks a lot like Australian Winter Peas and rye. Says it has chicory as well.
Why not stick with it if the deer prefer it ?
For the fall, you might give shot plot , pro graze or ultra forage all have Brassica which I think produces more forage per acre than anything I've seen to date. But don't count on it as a highly attractive plot until they figure it out. Which may take a while. I now have them eating it in the spring after a month of growth.
For the fall you might also try Australian Winter Peas (AWPs) mixed in with your oats and rye. Being in Fl, you can also get away with Iron/Clay or Soybeans planted in Aug, they should make it until late Nov through bow, muzzle and first few weeks of gun. Broadcast some rye, AWPs and brassica into it in Oct and when the peas/beans are gone or get frost bite, the rye , AWPs and brassica will keep going.
For the spring, not much beats soybeans , iron/clay and a little corn/sorghum for them to climb on. Use plot saver for 6-8 weeks and you should be good to go through July/Aug unless itís a small plot. BioMaxx seems to be some good stuff but isn't cheap. I have some going and the corn is starting to take off, hoping with recent rain the beans will catch up.
The other option is clover which I have not gotten to grow well down here yet, but working on it.