Is it possible to charge 3 parallel batteries without sending charge to the UPS?
My thought would be to leave all 3 batteries connected to the UPS at all times plus add a 'proper' lead-acid charger as well.  This charger would be a proper 2-stage or 3-stage charger with automatic float - equalization switching.

However, you need to be aware of a probable safety issue: the batteries are most likely LIVE with respect to ground when the UPS is connected to the incoming AC Mains.  That's because there is NOT any isolation from the AC Main in most low-power UPS units.

That's one of the reasons that the battery terminals are so well insulated in small UPS units.

You can use an external charger but you must ensure that the charger can withstand being at a voltage significantly above ground and you must ensure that no one can touch the battery terminals while the system is live.