Hey @Jackson Abbeduto,
Here's what I think you can do: build a 500 sq ft addition to your main house (assuming you have enough remaining allowable floor area left -- more on that below), and convert it to a JADU. There might be a way to get a second SFH on the lot too but I'm not 100% sure.
Here's some more info:
Second SFH:
I'm assuming you're in LA City. There's a great little summary pdf that will help you understand their zoning requirements: https://planning.lacity.org/od...
The table does say that you need 2500 sq ft of property area per dwelling unit, however if you go to the zoning code, there is an exception:
"Provided, that where a lot has a width of less than 50 feet or an area of less than 5,000 square feet and was held under separate ownership or was of record at the time this article became effective, the lot may be occupied by any use permitted in this section, except those uses requiring more than 5,000 square feet of lot area. In no case, however, shall a two-family dwelling or two-family dwellings be allowed on a lot with an area of less than 4,000 square feet."
I'm not entirely sure if this means you actually can build a second SFH, but you should do a virtual appointment with a planner and bring this up and see what they say.
The <5000 sq ft lots you're seeing with duplexes on them may have been built before current zoning laws were put in place. If they're new construction though, then they are either using that exception above or perhaps those lots did get a variance (fyi variances take something like 9 months and cost something like 10-20k to get, if I'm remembering correctly).
ADUs on Multifamily Lots:
The state law for ADUs does allow up to two ADUs on a multifamily lot, but it has to have a multifamily structure already on it, and their definition of multifamily is 2 or more attached dwelling units. So, unfortunately, this won't work for you right now either.
JADUs:
It looks like your only other option is to build a JADU, but a JADU must be converted from existing permitted square footage. Therefore, you first would need to build an addition, and then convert it to a JADU. JADUs can be a max size of 500 sq ft, and there is an owner occupancy requirement (meaning, you would have to sign an affidavit stating that you live on site.) To figure out if you can build a 500 sq ft addition, you will have to do the following: take the lot area, subtract the required setbacks, multiply that remaining area (called the Buildable Area) by 3 (because that's the FAR for R2 zones in LA City), and then subtract the area of your house and ADU. My guess is you will have more than enough remaining area to build the 500 sq ft addition.
Our company (Otto ADU) does ADUs and JADUs, as both garage conversions and new construction. We haven't done anything exactly like this before, but we are always open to new challenges. Even if we're not the right fit for the project (we're more design oriented and we do all design, permit, construction management, and procurement), we can try to answer questions and help you out.