This is a pretty cool project.
I've actually swapped four UPS units with lithium batteries, but I went with LiFePO4 for a number of reasons. For me the most important factor was safety. UPS units get ignored and forgotten about until they fail, so I wanted a chemistry that can take abuse without becoming a hazard. LiFePO4 is much more stable and doesn't usually exhibit thermal runaway.
The second was voltage. 4s LiFe basically replaces lead acid as is. charging voltages are pretty much perfect. LiFe likes slightly more float voltage but the charge termination voltage is pretty much identical.
I have done a 12v and 24v unit the easy way, using NEC ALM12V7HPs which drop in as a replacement for 7 and 9ah SLA, with series strings up to 48v allowed and 60A continuous charge or discharge. my HP T1500 G2 has a 36v 12s4P A123 pack from an EMC standby power supply. I ripped out the BMS and put in a daly 60A. it doesn't fit inside but sits next to the unit.
my most recent project is a Tripp-Lite SU2200RTXL2UA. I used 16 Headway 38120 cells and a 100A daly BMS. This unit is a beast and I even fit all the cells in the battery slot with 3d printed holders, though I am still having trouble finding room for the BMS. at full load the current is only 34A, so maybe I could have gone with a 60A and had room for it alongside the cells.
I see your mention of wanting to use lifepo4 but discharge rates being an issue. Everything I used up until the most recent headway pack is using A123 cells, which were absolute beasts that could handle 60A continuously and 120A peaks. the NEC batteries were manufactured by A123 and the BMS could cope with quite a lot. it's sad that the drop-ins available now are mostly only rated for a 1C discharge due to using anemic BMS boards. I have a 4s3p pack of super old A123 cells back when they used a cardboard wrapper and it still is in good shape and I have seen it put out 200A starting my friend's miata.
the charging voltage of my SU2200 would also be perfect for 13s of 4.2v lithium cells, but I'm just not comfortable having >500wh of normal lithium batteries in my house.
your shunt regulator is especially interesting to me, as it could handle a charge circuit that was just a low float current and had far too high of an OCV.