LiFePO4 in parallel with solar charge controller?
The following depends somewhat on specific attery characteristics and needs to be verified either with manufacturer's specifications or by testing. 

It's likely that the LiFePO4 CAN safely be floated at higher than you show but somewhat below normal Vchgmax - so that Ichg is zero. 
LiFePO4 has a charging terminal voltage of about 3.6V 
so 4 cells = 14.4V 
= above the 13.5V MPPT output that you show. 
13.5V/4 =~ 3.4V/cell which is at about the 3.2V you are liable to get at light load fully charged. 

You will need to look at what the manufacturer says BUT
1. 13.5V is probably a safe float voltage once charged
2. 13.5V is NOT enough for a full charge.
Given the above, if you can change the MPPT voltage under program control you can probably do CCCV charging to desired endpoint, then float at about 13.5V with or without load attached. 

Actual LiFePO4 Vout without any PV depends on battery, SOC and load but is usually in the 3.0-3.3V / cell range (3.3V only at very start).
You can go lower but usually remaining capacity is minimal (except at very high loads.) 

While LiFePO4 SOC can notionally be safely taken very low (0% according to some) I note that long lifetime warranties offered here are dependent on SOC never below MUCH higher levels and NEVER below 20%. 

Extra: You can charge LiFePO4 in CC only mode with Vmax trip of about 4.0-4.1V/cell. TI do this in some of their charge ICs.
If charged at CC then Vbat rises much as expected to about 3.6V per cell then rises far faster to Vmax. SOC goes for 9x% to 100% over this last voltage range. I have observed this action but do not have good data for relative SOC across this range but if you coulomb count AND keep Vmax below say 4.0 to 4.1V/cell then "you should be OK" (YMMV). (Coulombic efficiency of LiFePO4 (and LiIon) is > 99%).
You'd ideally be monitoring per cell voltage if doing this - as you mention that you intended to do.  

You can probably top balance quite well due to the above LiFePO4 characteristic. Due to the low capacity in the 3.65V - 4.0V range you can easily hold cells which reach say 4.0V at that voltage by shunting charge current while the others 'catch up'.