Couple things.
1) Agm batteries need a higher voltage to fully charge, 14.8 rather than a normal lead acid of 14.4. I can't remember if these charge correctly (fully) in the 4runner system, it might not fully charge at all, ever. Deep cycle has nothing to do with it, it's the fact it's an AGM battery and they take that higher voltage to top off.
2) Looks like you have a 100 amp hour battery there, however your charger your using (the 7002) only charges at a max of 7AH. So, it would take close to 15 hours to fully charge that battery from that charger if the battery were fully dead so 3 hours is not going to fully charge it unless it was almost full.
3) I'm confused on why your fridge would need to be disconnected. That charger only goes to max of 15.7 volts, and not sure about your fridge, but my fridge (Indel) can use input voltages up to 24 volts, so having the voltage fluctuate with the charger really shouldn't hurt anything.
4) The alternator is capable of 130 amps output and around 70-80 amps output at idle. you can fully charge a normal lead acid battery from dead very quickly from the stock alternator even at idle. output of the alternator should not be a problem.
5) I'm confused on how you are charging this, looks like your using the charger on the main battery using the existing main battery terminals to fuel the charger. I suppose this might work, but this just seems wrong to me, I would only think you would want a charger that like in a dual battery situation charging the isolated second battery, never the main. Perhaps this is the solution for stock vehicle with AGM installed in order to get the battery topped off, however still you will need it charging for a while at 7AH charge.
Of course, this is just my opinion, could be wrong, I'm still running the stock battery in my runner.