A few things to consider. Since transfer time is a concern:
"The transfer time depends on the UPS technology, and falls between zero and 12 milliseconds. The online UPSs have a zero transfer time while standby UPSs have an average of 8ms. The typical transfer times are: Standby UPS: 5-12 ms, – average 8 ms".
Next is a UPS can use any of several outputs. The preferred and slightly more expensive is a TSW (True Sine Wave) output which is what AC mains have, a true sine wave. Next is a MSW (Modified Sine Wave) output which closely resembles a square wave. Whatever your power supply is it needs to be compatible with a MSW output or whatever output your UPS has.
"Since all the equipment can be powered from 12Vdc and less, I was thinking of replacing the ups with a 12V lead battery (?) of around 10Ah and am looking for a reliable system to have it continuously charged while there's no outage, ideally, something actually in operation flawlessly for a long time.
Expected current out of the battery is ~2.5A"
With that in mind a 10 AH 12 Volt SLA battery will last about 4.0 hours. A common approach is just to place a battery tender on your battery and leave it there. During the cold winters here in NE Ohio US I leave a battery tender on my motorcycle 24/7 and maybe once a week I start and run the bike for about 15 min. The tender keeps my bike battery topped off. If you go this route shop wisely. I have seen the same 750 mA to 1.0 Amp tenders go from $20 USD or less to $99 USD for the same identical units. I have a few of the $19 ones which work just fine and I leave them connected 24/7.
You need to decide how large of a battery you want?
I use several UPS units all made by APC which serve us fine but they run less than a min during a power outage before the whole house generator is up and running. If all you want is 12 VDC I see no reason to recreate mains voltage only to reduce it to 12 VDC. Also, it doesn't hurt to place a large cap in front of your load. Especially if using a UPS and transfer time is a concern.