The other thing that makes me uncomfortable about your suggestion is:
If we combine the existing 12V deep-cycle battery with a new 12V
battery to make a 24V system for the trolling motor, we will only have
one battery left to do everything else (starting motor, powering fish
finder, VHF radio...etc), right? Unless I am misunderstanding
something, I will be very hesitated to do that. Please clarify.

Jay, My SeaPro uses 3 ea 12 v batteries tied to a Perko switch. Two
are primarily for the trolling motor and one is for starting etc. The
primary starting battery is tied to position 1 on the switch while one
battery for the trolling motor is tied to position 2. Should you
encounter problems with the primary battery you can switch to position
2 and use one of the trolling motor batteries (you can also charge
this battery under way in position 2). This will allow you to use two
batteries for a 24v system as well as have a back up. I also had a 3
bank charger installed so I can hook to 110v and charge all three
batteries (power cord runs to a plug on the side of the console). All
I have to do is plug an extension cord into the plug on the console
and all three batteries are charged simultaneously.