Hi Peter,
The Setec is a trickle charger with a max voltage limit set at 13.8v, is that correct or am i confussing this unit with another transformer device?
What is a TLS solar regulators? do you have a link to specs etc, one for the Setec might be good as well.
I wouldn't go to a MPPT controller but you already know my views on the shame regarding this technology being suited to low voltage small capacity solar systems

it rivals Dupont and the R134a scam, every one has been sucked in.
If you choose to fit a DC to DC charger it must have a proper Gel battery charging regime, max 13.8v, not the Gel battery killer charging regimes some charger manufacturers try to push on unsuspecting customers
As far as a BMS, every battery nees a BMS, it's a battery management system, but it doesn't have to be an automated high $$ item, they can be far more trouble than not using one, far more cell deaths can be directly connected to the use of a propriety BMS than any other cause, far better to use the smartest computer system we have available, the one between the ears, it has adaptive learning. You do need to monitor cell voltages (a proprietary BMS system doesn't) you do need a system to either warn you that cell voltages are too high or too low so you take the appropriate action, the next level up is for the warning system to turn something off, either the charger or the load, but that's about it. Cell balancing is done in the first cell conditioning stage, if you followed the directions you will probably never have to do it again, once every 3 mths at the very worst and a 5 min job even then. Mine have worked hard 24/7 for 18mths now (260Ah plus overnight) and are still perfectly balanced.
So,
A controller with fully adjustable voltages and stages is required as a solar controller, my recommendation is a good PWM controller.
A mains charger that has a suitable charging regime that is limited to 13.8v
If a DC to DC charger is used, it must be able to be limited to 13.8v
A cell logger and alarm to warn you things have wandered outside acceptable ranges.
Add ons that will make life easier:
A battery monitor, preferably one with an output that can switch a relay at adjustable state of charge (SOC) points
A relay system that can turn charging and loads off that can be driven by the cell logger and/or the battery monitor.
Ideally:
A controller that is also a battery monitor and capable of switching loads and charging off from all methods of charging, they are available and not all that expensive, one is Aust made, can you guess which one that is
T1 Terry