Let me start by pointing out that you haven't told us the capacity of the batteries, and that paralleling the batteries simply increases capacity, but does not provide redundancy or resilience. The voltages quoted suggest the batteries are, so to speak, undercharged, a 12V lead acid battery with a constant float charge would normally be over 13V and given a decent size battery, a 250ma discharge current for a couple of seconds would/should not cause a measurable drop in voltage.
The lack of charge control, for me is a non-issue - I've seen commercial products (solar powered marine navigational aids) intended to operate unattended with the panel and the load connected directly to the battery, the charge control as such is managed by sizing the panel to suit the load - that said, I have also seen that very system overcharge the battery, and when I engaged the manufacturer, was told that it could not happen, it was self regulating - I provided the voltage measurements taken, and a couple of weeks later, the company vice president (responsible for engineering) called me, they had units installed world wide, and were experiencing the overcharge problem in only two countries, Guyana (where I was located) and the neighboring island of Trinidad.
As I say it's for me, a non-issue, and since it's been working for years, I would say there's the proof.