While the power supplies are in constant-current mode, you should be OK. I would guess that your battery can absorb 7 kW, or you wouldn't be going to the expense of several power supplies. There will be slight differences between the currents from the different power supplies, but that doesn't matter. The situation should be stable even if the currents were very different. Each power supply is a high impedance current source feeding into a low impedance load.
There will be a potential problem when the battery is fully charged, which I assume it will happen at some point. The cut-off voltages of the power supplies will differ slightly, so they will all start to cut back the current differently. As each power supply starts to shut off, its output impedance falls. The situation is quite complicated, and modelling it is beyond my abilities, with four power supply impedances all falling from near infinite to near zero, all possibly at different times. The battery impedance will also have to be considered, and that will get larger as the battery ages.
You should also consider what happens if the battery becomes disconnected.
I'm not saying the set-up won't work, it's just difficult to be sure. Even if the power supply loads are unstable, which is far more likely when the battery gets charged, it may not matter. Certainly there are plenty of smaller battery chargers, and this includes car alternators, where the voltage control as the battery gets fully charged consists of turning the charging on and off quite quickly. (On car alternators it's damped by the field winding inductance so the alternator current changes little). I don't know what the effect of one or more 1.75 kW chargers turning on and off rapidly would be. Instability could be just a small variation in current, and it may not cause any adverse effects at all.