I of course will suggest SMA Sunny Island
(see my avatar picture)
That will manage GT PV inverters smoothly, using frequency-shift to adjust their power output (assuming they have that feature.) The shift from 0% up to 100% or back down takes a couple seconds, and Sunny Island will source or sink power from/to battery in order to make up the difference.
Other brands (SolArk, Outback, Schneider) have similar function, may or may not perform as well at this.
Sunny Boy GT PV inverter is best for the application because it can be set to "offgrid" where wider voltage and frequency are tolerated (good when using generator input), but any UL-1741-SA GT PV inverter that supports frequency-watts should work.
With two 120V Sunny Island configured for 120/240V split-phase, you can have up to 56A, 6.7kW per phase pass through to/from grid. So up to 13.4kW of micro- or string inverters, and loads. This could be for a protected loads panel, leaving larger loads on your 200A main panel. For double the pass-through current, four battery inverters could be installed.
You aren't likely to power electric furnace or range from the battery system, so not a big deal to not have whole house on backup. You can manually flip interlocked "generator" breaker to backfeed whole house panel during a power failure, just avoid using the electric furnace (which I have done inadvertently; I only have enough battery for an hour of that.)
The Enphase battery solution as you noted is expensive per kW of output (and kWh of storage).
Sunny Island and many others can use 48V lead-acid batteries, or lithium. For Sunny Island, particular model BMS allows communication. Some battery models are expensive, but others are more reasonable (maybe with a bit of DIY)
Sunny Boy Storage (an HF inverter) is 6kW with 9kW surge. Paired with an available (add-on) 200A transfer switch and auto-transformer, it can store power from your Enphase microinverters, pass through 200A for whole house, and provide backup. Of course, what it can power while grid down is limited. The catch is expensive 400V battery.
So assuming you want something like full home backup where you can at least decide which loads you want to run by turning off breakers, you have several problems to solve.
Let me suggest something simple and cheap. Get an off grid inverter. If you are running motors (like your heat pump), find one that is a low frequency inverter with a transformer in it. Something like a 12K growatt. They are around $2000.00. Then buy an inverter generator that can run on propane. To operate off grid yiu will need a way to disconnect. A generator breaker interlock would allow this.
With an inverter/charger, it can be fed by a breaker from main panel, keeping battery charged and connected to a critical loads panel, so things like alarm/communication are always powered.
With a backfed interlocked "generator" breaker, main grid breaker is turned off and inverter output fed through "generator" breaker to panel. Also, manually turn off the breaker which had been feeding the inverter/charger. You now have an off-grid system. If the inverter supports AC coupling, your Enphase or string inverters operate, supplying loads and charging battery.
I set up mine like that previously. First, GT PV. Then, with Sunny Island powered by main panel and manually feeding main panel (my multiple GT PV inverters were already on a separate breaker panel.) Then I moved the input breaker onto a line-side tap, so battery inverter + GT PV inverters + protected loads are always fed from grid. Main panel always fed from grid, except if I manually switch it to be fed from battery inverter.